The club made a u-turn on Monday to sign the Manchester United midfielder on loan but had to wait for it to be rubber-stamped.
Villa had initially pulled the plug on a permanent deal for Cleverley due to wage demands.
He was also believed to favour a switch to Everton, but the Toffees failed to strike a deal with United on deadline day.
That prompted Villa to reignite a move for the 25-year-old and they are waiting to see if they managed to complete it in time.
Villa had agreed a fee of around £8m with United for Cleverley but called the deal off on Monday after talks reached a deadlock.
He also sold Karim El Ahmadi back to Feyenoord and loaned Aleksandar Tonev to Celtic.
Cleverley looks to have little future at Old Trafford with boss Louis van Gaal making him available and Hull were also interested before moving for Newcastle's Hatem Ben Arfa.
The England international has made 79 appearances for United, the last coming in their 1-1 draw at Sunderland in August.
- Manchester United