They're also reporting that the season-long loan can be broken off in January if either party see it appropriate.
Cleverley was subject to an £8 million bid from Villa as they sought to bring the England international to Villa Park on a permanent basis.
Everton were also said to be interested in signing the 25-year-old as United looked to offload the midfielder prior to last night's deadline.
The move will present an opportunity for Cleverley to prove himself in the Premier League after having a difficult 18 months or so at Old Trafford having come in for a lot of criticism.
The reason the deal hasn't been announced was because Villa reportedly went in for a loan deal at the latest possible stage after discussions over a move to Everton had collapsed for the midfielder. Cleverley was reportedly at Manchester United's Carrington training ground until 2am trying to secure the move.