The young Englishman has struggled for minutes under manager Arne Slot and looks to be moving on for a more prominent role at Villa, who have been trying to add attacking recruits all window.
Elliott was named Player of the Tournament for England at the U21 European Championships in the summer and won the Premier League last season with Liverpool.
The 22-year-old joins fellow deadline day signings Victor Lindelof and Jadon Sancho