However, the 25-year-old could go back to United in the next transfer window in January or even be bought outright by Villa if his term there is successful
The deal was struck late on transfer deadline day on Monday and the clubs had been waiting for it to be passed by the Premier League's board.
Cleverley enjoyed successful loan spells at Watford and especially Wigan Athletic before gaining a regular first-team spot under Alex Ferguson in his final season in charge in 2012/13.
However, his fortunes have dipped in the past year, losing his place both in the United starting line-up and as a result the England squad.
Cleverley has played only one of United's four games this season in what has been a poor start to manager Louis van Gaal's reign.
And with several new high-profile arrivals, van Gaal, who is trying to revive a side who recorded their lowest league finish since 1990 last season, is willing to let the midfielder leave Old Trafford.
Cleverley, who has made 79 appearances for United, had also been linked with a move to Everton.
Source : AFP
Source: AFP