Both clubs announced the deal on Monday as Barkley became Villa's fifth signing of the summer.
Neither team disclosed the details of the deal but multiple reports suggest Barkley has penned a three-year contract at the Premier League club.
The 30-year-old is set for his second stint at Villa Park following a loan spell from Chelsea during the 2020/21 season.
Barkley will join a Villa side who finished fourth last season and will compete in the Champions League this term.
"With additions to the already great squad that we've got, it's going to be pivotal for the season," Barkley said following the switch.
He played a key role for Luton last term, making 32 league appearances, scoring four goals and registering two assists as the Hatters eventually went onto suffer releagtion to the Championship.