Watkins was the Championship's joint-top scorer last season with 26 goals.
The 24-year-old is Villa's second signing of the transfer window following the £16m arrival of defender Matty Cash from Nottingham Forest.
"Ollie has developed into one of the most sought-after strikers in the country," said Villa boss Dean Smith.
"We are looking forward to seeing him show his great qualities in an Aston Villa shirt.
"He is a hugely determined character who has both the ability and personality to succeed at the highest level."
Watkins will be reunited with Smith, who signed the forward from Exeter when he was Brentford manager.
The fee for him is a record for a Championship player. Although Manchester City paid Bournemouth £40m for Nathan Ake last month and Tottenham spent £30m on Newcastle's Moussa Sissoko in August 2016, neither had played in the Championship before moving back to the Premier League.
"I want to do something special here and score some goals."