The 22-year old defender has penned a three-year deal with the Birmingham club after a successful individual season in making 30 appearances last term.
"I'm really happy to have signed and for my future to be with Villa," said Baker.
"It's an exciting time and, because I've come through the academy as well, it's something that's really special to me, something that hopefully I can use as an inspiration in the future.
"We were probably one of the youngest squads in the Premier League last season and we felt that we got stronger and stronger as the season went on.
"The fans could see the progress we were making and they got behind us really strongly. That was felt very keenly by the players.
"Hopefully, next season we can keep improving and we can be even better. I think things are in place that we can really do that."