Fakhar Zaman, Mohammad Hasnain, Mohammad Rizwan, Shadab Khan and Wahab Riaz are also set to join the team in Worcestershire, the Pakistan Cricket Board (PCB) confirmed on Tuesday.
Pakistan are due to play three Tests and three T20Is in England, but preparations for those matches were plunged into doubt after 10 players tested positive for COVID-19.
However, a PCB statement said: "Fakhar Zaman, Mohammad Hasnain, Mohammad Hafeez, Mohammad Rizwan, Shadab Khan and Wahab Riaz have tested negative for Covid-19 for the second time in three days and, as such, are now eligible to join the Pakistan men's national cricket team in Worcestershire.
"The players were retested on Monday, 29 June, following a first negative test on 26 June.
"The PCB will now start making their travel arrangements and the departure details will be shared in due course."
Kashif Bhatti, Haris Rauf, Haider Ali and Imran Khan tested positive for a second time earlier this week.
The rest of Pakistan's travelling party arrived in Manchester on Sunday and underwent testing prior to a 14-day isolation period in Worcestershire.
On Tuesday the PCB said seven of its team members and a masseur had tested positive, with three others having been found to have the virus on Monday ahead of a scheduled tour to England.
However, on Wednesday Hafeez claimed he did not have coronavirus, tweeting a picture of a test result that showed he was negative.
The all-rounder said he and his family got the all-clear after seeking a second opinion.
England and Pakistan are due to play three Tests and three Twenty20 Internationals from the end of July until September.
The PCB said the latest players to test positive, aside from Hafeez, were Fakhar Zaman, Imran Khan, Kashif Bhatti, Mohammad Hasnain, Mohammad Rizwan and Wahab Riaz, along with masseur Malang Ali.
In a statement, the PCB said its medical panel was "already in contact with these players and the masseur, who have been instructed to observe strict quarantine at their homes for their and their families' wellbeing".
It remains to be seen if Hafeez's latest result will allow him to be free of the same quarantine restrictions.
The Pakistan Cricket Board (PCB) released a statement to reveal the list of names who will be on the chartered flight to Manchester, as well as an update on the situations of those who had previously tested positive for COVID-19.
Of the original 29-man squad, 18 received the all-clear following Thursday's checks, as well as 11 members of the support staff.
They will be joined on the journey by fast bowler Musa Khan and wicketkeeper Rohail Nazir, who have also been tested twice in the past week. Zafar Gohar, meanwhile, will team up with the squad on their arrival in England.The left-arm spinner played a solitary one-dayer for Pakistan in 2015, though he will only be involved in pre-match preparations.
As for those not making the initial trip, they will not be able to travel until returning two successive negative results.
Six players - Fakhar Zaman, Mohammad Hasnain, Mohammad Hafeez, Mohammad Rizwan, Shadab Khan and Wahab Riaz – have done so once and will be tested again next week with a view to joining their team-mates.
Haider Ali, Haris Rauf, Kashif Bhatti and Imran Khan, along with masseur Malang Ali, all tested positive again, however. The PCB medical team has instructed them to remain in quarantine, with their progress to be monitored.
"I want to reassure the players and the official left behind that the PCB will provide them the best support and look after them during the quarantine period," PCB chief executive Wasim Khan said in a statement.
"It needs to be remembered that these players were asymptomatic, which means their chances of regaining complete fitness are higher and brighter than most. As soon as these players test negative twice through the PCB testing process they will be flown to England to join the squad.
"I am aware Mohammad Hafeez and Wahab Riaz took personal tests outside of our process prior to the second PCB testing. While their results came up negative, as per the PCB testing programme, they are deemed to have one negative test following a positive test.
"Therefore, once they are retested and receive a second negative result under the PCB testing programme, they will be available to join the squad in England."
Pakistan are scheduled to play three Tests and a trio of Twenty20 fixtures against England.
Pakistan squad travelling to England: Azhar Ali (captain), Babar Azam, Abid Ali, Asad Shafiq, Faheem Ashraf, Fawad Alam, Iftikhar Ahmad, Imad Wasim, Imam-ul-Haq, Khushdil Shah, Mohammad Abbas, Musa Khan, Naseem Shah, Rohail Nazir, Sarfaraz Ahmed, Shaheen Shah Afridi, Shan Masood, Sohail Khan, Usman Shinwari, Yasir Shah.
England are set to face Pakistan in three Tests and three T20 internationals across July and August but the tour was thrown into doubt over the past week as the initial 29-man touring party was struck by a raft of COVID-19 cases.
Haider Ali, Haris Rauf, Shadab Khan, Fakhar Zaman, Imran Khan, Kashif Bhatti, Mohammad Hafeez, Mohammad Hasnain, Mohammad Rizwan and Wahab Riaz all tested positive.
The ECB said in a statement that players testing positive will not be allowed to travel with the advanced group, with Hafeez's status unclear after the all-rounder tweeted a picture of a negative test and claimed he had received the all-clear.
Test captain Azhar Ali, white-ball counterpart Babar Azam and the remaining players will use Worcestershire's New Road as their training base during their mandatory 14-day isolation period before transferring to Derbyshire's County Ground.
Bilal Asif, Imran Butt, Musa Khan and Mohammad Nawaz have been named as reserves for the Pakistan squad and could make the trip subject to returning negative coronavirus tests.
England's home season has been delayed by the global pandemic but they will host West Indies at the Ageas Bowl next month in the first of three Tests.
The all-rounder played in 392 matches for his country in all formats, including 55 Tests, with his final appearance coming in the semi-final defeat to Australia at the Cricket World Cup.
Hafeez, who was captain for 32 international matches, scored 12,780 runs and took 253 wickets in an 18-year Pakistan career that began against Zimbabwe in Sharjah on April 3, 2003.
Ranked the number-one Twenty20 all-rounder by the ICC in 2014, Hafeez was described by Pakistan Cricket Board (PCB) chairman Ramiz Raja as "a wholehearted cricketer who worked tirelessly at his game to have a long and fruitful career".
Hafeez said: "Today I say goodbye to international cricket with pride and satisfaction. In fact, I have earned and accomplished more than I had initially envisaged and for that, I am thankful to all my fellow cricketers, captains, support staff and the Pakistan Cricket Board who helped me out during my career.
"And, of course, my family who made big sacrifices to ensure I achieved my aspirations of representing Pakistan at a global stage.
"I am extremely fortunate, lucky and proud to have been considered worthy of donning the national kit with Pakistan emblem for 18 years. My country and my team have always been at my forefront and therefore, every time I stepped on to the field, I tried to raise their profile and image by playing hard and tough but within the rich traditions of spirit of cricket.
"When you have a professional career as long as mine, you're bound to have your share of highs and lows, and I was no different. Results apart, I can say with conviction that I had more highs as I had the privilege of playing with and against some of the finest exponents of the bat and the ball of my era.
"While cricket has been a great learning school for me, this great sport has provided me opportunities to visit various countries, explore their cultures and make friends. These are lifelong memories, which I will cherish every day. I want to thank my fans and supporters for believing in my abilities and backing me throughout my career."
Hafeez was recalled for the upcoming three-match T20 series against Bangladesh on Thursday.
The 39-year-old revealed a day later that he will end his long international career after gracing one last major tournament in Australia, if selected.
"It has been a privilege," Hafeez told media.
"I want to play the T20 World Cup and then exit from Pakistan's international team."
Hafeez ended his Test career in December 2018 after playing 55 times in the longest format, having scored 3,652 runs - including 10 centuries - and taken 53 wickets.
The veteran has appeared in 218 ODIs, making 6,614 runs and claiming 139 scalps, and has played 89 times in the shortest format - picking up 54 wickets and amassing 1,908 runs.
Hafeez has been banned from bowling in international cricket on three occasions due to an illegal action.
He added: "I have played 17 years for Pakistan and tried my level best. At times I missed my bowling."
The T20 World Cup commences on October 18.
The picture, taken on the golf course adjacent to the on-site hotel at the Ageas Bowl, was posted on the Pakistan all-rounder's Twitter page on Wednesday.
The course is part of Pakistan's bio-secure bubble but interaction with others is not permitted as per social distancing rules and former skipper Hafeez, who is not a part of the Test squad but there for the limited-overs leg of the tour, must now await the results of a fresh coronavirus test.
Pakistan said in a statement: "As it was evident from the photograph that Hafeez had breached the two-metre social distancing protocol and following a consultation process with the team doctor, the team management has decided to isolate him until he returns a negative Covid-19 test.
"Hafeez underwent the Covid-19 test late Wednesday afternoon and the result is expected at some stage on Thursday. The decision to put Hafeez in isolation has been taken for his and, the safety and security of everyone around him.
"The team management believes it was an inadvertent mistake, but a good reminder for everyone on the importance of following the bio-secure protocols, which have been designed for the health and safety of everyone involved in the series.
"The team management has updated the England and Wales Cricket Board of its decision."
Meanwhile, Pakistan have named an unchanged squad for the second Test of their three-match series with England, which they trail 1-0 following an agonising defeat at Old Trafford last week.
The tourists were undone by a stand of 139 between Jos Buttler and Chris Woakes in their first match back in six months because of the coronavirus pandemic, going down to a three-wicket defeat.
England pulled off their highest run chase against Pakistan to take a 1-0 lead on Sunday, but they fell just short to go down by five runs two days later at Old Trafford.
The in-form Hafeez (86 not out off 52 balls) smashed his joint-highest T20I score, including six sixes, and teenager Haider (54 from 33) marked his international bow in style as the tourists posted 190-4 after being put in.
Moeen Ali returned to form with a blistering 61 off 33 balls, but Shaheen Afridi (2-28) and Wahab Riaz (2-26) starred with the ball to deny England a sixth consecutive T20 series win.
Pakistan will head out of the bio-secure bubble and back home with a deserved first victory of a two-and-half month tour, while England welcome back regulars for a series with Australia.
Moeen bowled Fakhar Zaman with his first ball and Tom Curran reduced Pakistan to 32-2 by cleaning up captain Babar Azam (21), but a stand of 100 between Haidar and Hafeez set them on their way to another big total.
Haider struck his second ball in international cricket off Moeen for six and was particularly strong off his legs as he raced to a magnificent half-century off only 28 balls.
Hafeez took just 31 deliveries to bring up another 50 as he cleared the ropes with apparent ease - including twice in as many balls off Adil Rashid.
The veteran continued to dish out the treatment after Chris Jordan (2-29) removed Haider and England suffered a blow when the excellent Afridi bowled Jonny Bairstow in the first over of the run chase.
Dawid Malan (seven) and Eoin Morgan (10) scored match-winning half-centuries on Sunday but fell cheaply in the decider and Tom Banton followed leg before to Haris Rauf four shy of a second half-century of the series.
Moeen and Sam Billings (26) put on 57 for the fifth wicket before the latter was dismissed by the recalled Wahab, but the clean-striking left-hander powered his way to 50 off just 25 balls.
Sarfaraz Ahmed missed a straightforward chance to stump Moeen on seven and could only watch on as he cut loose, but England's chances were slim when he was caught and bowled by Wahab.
England needed 17 off the last over from Haris and, although Curran hit the penultimate ball for six, he was unable to repeat that off the last delivery as Pakistan edged it.
England pummelled by a combination of youth and experience
Hafeez was in sparkling form at the weekend and he lit up an empty Old Trafford again with a brutal knock, setting about the England attack with a combination of sweet timing and sheer power.
The 39-year-old was in great touch from the off and now has four half-centuries in his last five knocks for Pakistan in the shortest format - including three in a row.
While Hafeez is in the twilight of his career, 19-year-old Haider is only at the start and he should be around for a long time on the evidence of his classy knock, having looked very much at home on the international stage.
Majestic Moeen shows class is permanent
Moeen has been out of sorts with the bat and also failed to take a wicket in the ODI series against Pakistan, but he showed his class in Manchester.
He curiously only bowled one over despite a wicket with his first ball but returned to form in spectacular fashion with bat in hand.
Moeen launched four sixes and hit as many fours to give England a chance and, although they were beaten, the all-rounder should head into the series with Australia with a spring in his step.
Hafeez played with typical class as Pakistan, who lost the first of three matches by five wickets, to steer Pakistan to 163-6 in Hamilton.
But paceman Southee (4-21) took three wickets in the powerplay as Pakistan toiled to 33-3 and never found a partner able to stick around with Hafeez.
Seifert, fresh from a fifty in the first match, then smacked the ball to all areas of the ground, scoring eight fours and three sixes in his 84, while Williamson added 57 as the Black Caps reached their target with four balls to spare and nine wickets in hand.
Southee's first spell included a stunning outswinger that had the dangerous Mohammad Rizwan (22) caught behind, with Haider Ali (8) and Abdullah Shafique (0) quickly sent packing.
Hafeez judged the pitch to perfection, taking on singles early doors, before pummelling the short balls over square leg and sending the full ones to cover.
The issue was those at the other end offered little and New Zealand's reply saw the wonderfully gifted Seifert settle at the crease after an opening in which he swung and missed at plenty.
Anything Pakistan bowled short, Seifert would pull and cut away and – after Martin Guptill (21) – was dismissed in the fourth over, he had the perfect foil in Williamson, whose own knock included eight fours and a six.
New Zealand consequently hold a 2-0 lead ahead of the third and final T20 in Napier on Tuesday.
