Cleverley, 25, had been widely expected to leave Old Trafford in the transfer window, and moves to the Midlands for the duration of the 2014-15 season.
Everton and Hull City had been linked with a move for the England midfielder, but Paul Lambert has swooped to bolster his ranks after an impressive start to the season.
The transfer had to be ratified by the Premier League board as it was completed in the early hours of Tuesday morning, UK time, after the deadline had officially passed.
However, Cleverley will link up with Villa, who sit third in the Premier League after two wins and a draw from their opening three games, and could make his debut against Liverpool after the international break.
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