The former England fast bowler was appointed to the post in December 2021 in the wake of the racism allegations that rocked the sport.
Gough said: “It’s been an absolute honour to work for my boyhood club over the last two seasons.
“Having stepped in at a very challenging time, we’ve worked hard to steady the ship and develop our cricket department to ensure we can return to the top tier of English cricket.
“Following conversations with the club, I have decided now is the right time to step away from my role and give someone else an opportunity to take our playing squads forward.
“I’d like to thank all of our players, staff, members and fans for their considerable support over the last few seasons and wish them all the very best for the coming year. I will always be a Yorkshire Cricket supporter and look forward to returning to watch our teams in the coming years.”
A statement from Yorkshire said the club would take time to consider the best structure going forward before appointing any replacement.
Colin Graves, recently reappointed as chairman of Yorkshire, said: “I’d like to express our sincere thanks to Darren for the work he has put in over the last few seasons.
“Darren is a club legend in his own right having enjoyed two very successful stints as a player here and now helped us through some very difficult times.
“Everyone at the club would like to wish him all the best for the future, and we look forward to welcoming him back to Headingley again soon.”
The 29-year-old Barbadian’s signing will provide the team with well-needed experience said Yorkshire County Cricket Club Managing Director Darren Gough.
“He is a great signing,” said the former England fast bowler. “He brings so much experience – one thing we are lacking is just a little bit of experience so he just gives us that and comes into the squad for this first game.
“We felt we needed just the one experienced face in and we went for Shai. He has been playing well for the West Indies in one-day matches, he has got a record of playing Test cricket – he had his two hundreds at Headingley before for the West Indies.”
In 2017, Hope became the first player ever to score two centuries in the same first-class match at Headingly while playing the West Indies in a Test Match against England.
Hope, who 23 at the time scored of 147 and 118 not out as the West Indies pulled off a remarkable victory.
Brook has not played since December, having withdrawn from the Test tour of India and his planned stint at the Indian Premier League following the death of his grandmother Pauline.
Yorkshire had already indicated that the 25-year-old was likely to return early in the Vitality County Championship campaign and, following discussions with the England and Wales Cricket Board, have now confirmed his schedule.
Brook is ready to feature for the White Rose throughout April and the beginning of May, starting at home to Leicestershire on April 5 and taking in fixtures against Gloucestershire, Middlesex, Derbyshire and Glamorgan.
Thereafter, he is due to link up with England for their T20 series against Pakistan and June’s T20 World Cup.
After failing to win promotion from Division Two last year, Yorkshire’s chances of making serious waves in the second tier this year are further enhanced by the presence of former Test captain Root.
Having played a full part in the two-month Test tour of India he will miss the curtain-raiser at Headingley but then links up with the side for their next four fixtures, as well as the visit to Northamptonshire on May 24.
Head coach Ottis Gibson, who needs to see some improved results following Darren Gough’s departure as director of cricket, had earlier trailed the pair’s availability, suggesting: “Having those two playing for us would be special.”
