The striker has signed a three-year deal to join Villa for an undisclosed fee.
"He is also a top professional with a great character who will be a leader in our squad and a role model for our rapidly developing young Academy players who are now in and around the first team."
Ings scored 12 goals in 29 Premier League appearances last season, taking his career total in the competition to 55 goals.
In 2019/20 only Golden Boot winner Jamie Vardy bettered his total of 22 goals.
The 29-year-old becomes Villa's second signing of the day, following Leon Bailey from Bayer Leverkusen, and their fourth senior recruit of the summer transfer window.
He could make his Villa debut at Watford on Saturday 14 August.