The 25-year-old England international, unwanted by new United boss Louis van Gaal, clinched the deal with just moments to spare of the transfer window after a day of confusion almost saw the midfielder sign for Everton.
Sky sources understand Villa had a permanent deal set up for Cleverley to sign after he spent most of September 1 at the club's Bodymoor Heath training ground.
But a late move from Everton caused Cleverley to travel to Merseyside, only for that potentially permanent deal to fall through because Manchester United's representatives were too busy with other late deals.
Sky Sports believes the club were busy securing Radamel Falcao's loan move to Old Trafford from Monaco and Danny Welbeck's £16million transfer to Arsenal, as well as additional outgoings, to deal with Cleverley appropriately.
However, Villa remained confident of landing Cleverley after outlining to the Premier League that they had reached an agreement long before the last moments of the deadline and submitted the document before the window closed at 11pm.
Cleverley is one of a number of players, along with Welbeck and Shinji Kagawa, who returned to former club Borussia Dortmund, told by Van Gaal they would not be in contention for regular first-team football this season.