Carsley takes over from Aidy Boothroyd, who stepped down from his position in April after the Young Lions bowed out of the U-21 European Championships at the group stages.
England lost to Switzerland and Portugal in the group stages while victory over Croatia in their final game counted for nothing.
Upon his appointment, Carsley, who won 40 caps for the Republic of Ireland said: "I see it as a massive honour and achievement to coach the Under-21s.
"It is a really prestigious position with a lot of responsibility as has been proven by the calibre of predecessors in this role. Gareth (Southgate) and Steve Holland have always been very supportive and I am looking forward to working more closely with them.
"We have a great opportunity to help the senior side by developing the best young talent in this country while combining that with being successful at U21 level.
Cole will be taking charge of his first major coaching role since retiring from football in 2019. He won 107 caps for the England national team.
"I am really happy to get this opportunity to support Lee and work with the best youngsters in the country," Cole said.
"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."
