The two clubs reached an agreement on a deal late on Wednesday night, following several days of talks.
Mings, who also attracted interest from Albion and Nottingham Forest, becomes Dean Smith’s third signing of the transfer window after goalkeeper Lovre Kalinic and defender Kortney Hause.
There is an option to make the deal permanent at the end of the season.
Mings’s ability to play at either left-back or centre-half appeals to Smith and it is the latter position where the 25-year-old could feature most, with skipper James Chester still struggling with a knee injury.
At 6ft 4ins tall, the former Ipswich man will also add a physical presence to Villa’s backline.
He is unlikely to be Villa’s only signing of deadline day, though their hopes of landing Isaac Hayden from Newcastle have been hit by the reported collapse of the Magpies move for Benfica midfielder Andreas Samaris.
It now appears likely Hayden will not be allowed to leave the north-east during this window.
Villa are also interested in bringing in a striker, with Southampton’s Charlie Austin one of several targets.