The Scot, who played under Palace manager Ian Holloway at Blackpool, has signed a three-year deal with the Premier League new-boys after ending his lengthy association with Villa, which began when he joined the club's youth academy as a 14-year-old.
Bannan has since made 83 appearances, but has moved on after struggling for regular first-team football since the arrival of Paul Lambert.
And he has expressed delight after being handed a new opportunity by Palace.
"I went back home to Scotland over the weekend ahead of meeting up with the international squad so I've had to travel back down but it's a great bit of news for me," he told the club's official website.
"I was at Blackpool with the gaffer here when they got promotion that year and that was probably the highlight of my career so far.
"It is a big move for me to leave Villa and I would like to thank the fans there but it's a new chapter in my life now and I can't wait to get started.
"I want to get myself in the door and start training and hopefully get myself in the team. I haven't played this season and didn't much last year so I can't wait to get going."
Bannanmade his Scotland debut in 2010.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1