The versatile 20-year-old, who is the younger brother of United's Wes, becomes City's seventh new face this summer and arrives just 24 hours after Derby striker Callum Ball also sealed a season-long move to the Ricoh Arena.
Brown, who has enjoyed previous loan spells with Bradford, Doncaster and Oldham, will join up with his new team-mates next week.
Sky Blues boss Andy Thorn said: "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 6ft 3in, he's big and athletic and can play at the back and in midfield which is a big plus for us. The fact 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 another important signing for the club in what has been a busy summer."