Jose Mourinho has now won the League Cup four times, a joint-record among managers along with Brian Clough and former Manchester United boss Sir Alex Ferguson.
United played out a thrilling Wembley final with Southampton on Sunday, with Zlatan Ibrahimovic scoring twice to secure the trophy for the Red Devils.
Manolo Gabbiadini had an early goal ruled out for offside but went on to score twice, levelling the game after Jesse Lingard put United 2-0 up in the first half.
Ibrahimovic struck three minutes from time, though, securing United's fifth League Cup trophy, and Mourinho's fourth.
The Portuguese led Chelsea to the trophy in 2005, 2007 and 2015, with Sunday's victory his first major trophy as United boss.
Mourinho also became the first manager to win a major trophy in his first season at Old Trafford.