Carsley is promoted from his role with the England Under-20 team to replace Aidy Boothroyd, who has left after almost five years in the position.
Cole won 107 caps in an illustrious playing career and will be the chief support to Carsley, combining the position with his role as a coach in Chelsea's academy.
"I'm really happy to get this opportunity to support Lee and work with the best youngsters in the country," said Cole, who began his coaching career with Derby County.
"I loved playing for the national team and to now get the chance to work as an England coach is a special feeling.
"St. George's Park is an amazing place and I can't wait to get started. I want to do my best to help young players to develop, and also learn from some brilliant people at the same time."
Boothroyd left the Under-21 job on a disappointing note after failing to progress through the group stage of this year's European Championship.
He had taken the role, initially on a caretaker basis, in 2016 after Gareth Southgate was promoted to the senior team.
The new regime will start with matches against Romania and Kosovo in September.
FA technical director John McDermott added: "I'm very happy to be able to confirm Lee's appointment, and to be able to bring in someone of Ashley's stature as his number two, with thanks to Chelsea for their support."
Former Arsenal and Chelsea defender Cole, 40, has also worked as a television pundit since retiring as a player with Derby in 2019.
Arsenal forward Balogun has excelled on loan with Reims this season, scoring 17 goals in 27 Ligue 1 appearances – behind only Jonathan David and Kylian Mbappe (both 19).
The 21-year-old's excellent form has prompted talk of a tussle for his international allegiance, with the New York-born star eligible to represent England, the United States and Nigeria.
Balogun has been a mainstay in the England Under-21 set-up, but he withdrew from the squad for this month's internationals due to injury.
That development has led to fresh hope Balogun will pledge himself to the USMNT, and Turner confirmed he had spoken to his Gunners team-mate on the matter.
"I spoke to Flo. We obviously had most of our preseason together, and I knew going into it he had some roots in the USA," the goalkeeper said on Wednesday.
"So, he and I developed a relationship pretty quickly. That's pretty much the extent of it. We check in on each other here and there.
"He'd be a great addition to our national team. I think he's done really well, obviously, for his club on loan, and we'll see.
"The decision has to come from the heart, because it's not necessarily an easy task to come and play in these CONCACAF games. It's a tough region at times.
"So, for us, we'd be really grateful to have him, but his heart needs to be in it."
Earlier in the week, Balogun told Sky Sports he was yet to decide on his future but has aspirations of playing at the highest level.
"My international future is not decided yet in terms of who I'll play for," he said. "But of course I want to play international football at the highest level, in the World Cups, and I want to compete at the highest level.
"I want to put myself in positions where I'm performing in front of millions of people."
The Football Association has announced 16 players across England's senior men and women's teams, and the Under-21 squad, will take part in a competition that begins next week.
As well as underlining the importance of the United Kingdom government's advice for citizens to stay at home amid the coronavirus pandemic, the tournament will also highlight the National Emergencies Trust, a collection of community foundations that distributes money to charities.
Chelsea trio Mason Mount, Callum Hudson-Odoi and Tammy Abraham will also compete in the tournament, along with fellow England players Callum Wilson and James Maddison.
Lucy Bronze, Jordan Nobbs and Ellie Roebuck - all part of Phil Neville's women's squad - will also be involved, as will Under-21 internationals Reiss Nelson, Todd Cantwell, Max Aarons, Eddie Nketiah and Ryan Sessegnon.
The opening round of the tournament begins on Friday, April 10.
Bellingham left boyhood club Birmingham City for Dortmund at the end of the 2019-20 Championship season in a reported initial €23million (£21m) transfer.
The midfielder is yet to play a competitive match for BVB but has now been promoted from the U17 national team set-up.
Bellingham is the youngest player in an England U21 squad - named for matches against Kosovo and Austria - that also features Bukayo Saka and Josh Dasilva, both similarly stepping up to this level for the first time.
Arsenal's Saka is eligible to play for Nigeria but has been included by Aidy Boothroyd despite missing out on a senior Three Lions group which did not feature a single left-back.
Chelsea winger Callum Hudson-Odoi is the only player in Boothroyd's squad with senior international experience.
Sancho prevailed 2-1 despite initially trailing to a goal created by the in-game version of the Borussia Dortmund winger, his cross finding Rashford, controlled by Rashford.
"Oh, Jadon Sancho to Marcus Rashford! Sanch is under pressure right now," Rashford laughed on camera. "Oh my lord, I know you're sweating."
However, Sancho equalised through Rashford himself and then netted a winner with Raheem Sterling.
"I threw the game away, man," Rashford moaned, before adding: "You know what? I'm going to play you again. I'm going to go back to the drawing board and play you later."
Sixteen players across England's senior men's and women's teams and the Under-21s are involved in a tournament designed to raise awareness for staying at home during the coronavirus pandemic.
In the competition - which also highlighted the National Emergencies Trust, a collection of community foundations that distributes money to charities - Tammy Abraham, James Maddison, Todd Cantwell and Lucy Bronze were among the others to also advance to the quarter-finals.
Abraham was helped by a hat-trick from Rashford as he defeated Chelsea colleague Callum Hudson-Odoi 5-2.
Meanwhile, Maddison scored as himself in a come-from-behind 3-2 victory over Callum Wilson that was sealed with a winner from Harry Kane.
"Look who it is! The dangerman," Maddison cried after finding the net with his computerised self.
Cantwell won the battle of the midfielders against Mason Mount, with substitute Rashford scoring a hat-trick in a 5-0 win after the Norwich City man brought him off the bench.
Mount had threatened to quit if Cantwell scored with the virtual version of the Chelsea midfielder, though he vowed to retire from the game after the drubbing.
"Go and win this and I won't feel bad," he told Cantwell.
Cantwell's club team-mate Max Aarons had his own hat-trick hero as Maddison grabbed all the goals in the 3-1 victory over Trent Alexander-Arnold's England.
Elsewhere, Ryan Sessegnon won 3-1 against Reiss Nelson, who was in disbelief that it was only a one-game series, while a golden goal earned Bronze a victory over Ellie Roebuck.
Bronze is the only female representative in the last eight after Eddie Nketiah saw off fellow Arsenal star Jordan Nobbs, setting up a meeting with Sancho.
