The Sweden captain spent eight seasons at Old Trafford, after arriving from Benfica in 2017, but his contract expired in the summer.
Aston Villa have snapped up the central defender, with Unai Emery's side confirming his signature on transfer-deadline day.
The 31-year-old made 284 appearances in total for the Reds.
One of his four goals actually came against Villa, during a 2-2 home draw with the Midlanders, in December 2019.
Lindelof could make his debut for his new club in their next fixture, the Premier League away game at Everton on Saturday 13 September, following the international break.