Bannan has signed a three-year deal after the clubs agreed an undisclosed fee to reunite him with Ian Holloway following a loan spell with Blackpool in 2010.
"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 Palace Player.
"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."
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