"I'm delighted to be awarded the T20 captaincy. The role is one that I have really enjoyed," Morgan said.
"We've got an exciting group of players here at Middlesex, with plenty of talent and a good blend of youth and experience, and I'm really looking forward to helping the club build on the improvements we made in this format last year," he added.
Middlesex last year reached the quarter final stage of the competition for only the second time since it lifted the trophy in 2008.
The left-handed batsman played a crucial role in helping to transform Middlesex's T20 Blast fortunes last season, hitting three half centuries in the competition - 70 off 37 balls against Surrey at Lord's, a brilliant unbeaten 83 off just 29 balls against Somerset and a gutsy 53 off 31 balls in the quarter-final defeat to Nottinghamshire.
He finished the 2019 tournament with 341 runs at an average of almost 43 and a strike rate of just under 170.
Hailing the 33-year-old as the best limited-overs captain in world cricket currently, Middlesex head coach Stuart Law is hopeful of his side putting up a challenge in the T20 Blast this season. "I'm really excited to have Morgs at the helm for our T20 campaign," Law said.
"He is currently the best white-ball captain around and will offer a great deal of experience on and off the field to the team in this format. I can't wait to start working with him to build a squad of players to challenge in this format," he added.