The 20-year-old has yet to play a first-team game for the Red Devils but has had loan spells with Oldham, Doncaster and Bradford.
City manager Andy Thorn is delighted to have sealed a deal for the youngster and is hoping he has the same impact that fellow United player Ollie Norwood had at the Ricoh Arena last season.
He told the club’s official website: "This is another really good signing for us. Reece is a massive talent and we are delighted to be able to bring him here for the season.
"At six foot three, he's big and athletic and can play at the back and in midfield which is a big plus for us.
"The fact that we looked after Ollie Norwood so well last season has stood us in good stead with Manchester United and we are grateful that Sir Alex Ferguson and his staff have put their faith in us to do exactly the same with Reece.
"This is another important signing for the club in what has been a busy summer."
Coventry will play in League One in the upcoming season after a 23rd-place finish in the Championship last campaign.