The deal for the Clermont Foot defensive midfielder is reportedly worth around £2 million and he represents Paul Lambert's first signing of the January window.
Sylla told the club's official website: "I'm very excited about the prospect of playing for Aston Villa and also to be playing in the Premier League.
"I have watched some games here on TV back in France and a player such as Cheikh Tiote, who is strong and forceful, I admire his style of playing.
"The manager is building a dynamic and exciting young team here and there are players also with a lot of experience. Obviously, I know plenty about Charles N'Zogbia, with him being French as well, and it will be great to play alongside him.
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"I know some of the other players here, too. Christian Benteke has had an extraordinary season so far. For such a young player to have made his name in the Premier League already shows there is real quality here at the club and I'm excited by this.
"I can't wait to fight for the club and help the club to climb the table. My first task will be to integrate myself with my new team-mates and to help those around me to grow and to build with them a strong team. I'm thrilled to be part of this.
"Playing at Villa Park will be unbelievable. It is a huge stadium with a great history and the crowd will be incredible. You dream about this when you become a footballer.
"I can hopefully help the team when we're defending against our opposition and to get the ball moving forward. I know the fans are very passionate and it will be great to get started as soon as possible.
"The club has made me feel very welcome already. The facilities at the training ground are first-class and I will be very proud when I put on the shirt and play my first game. I am looking forward to this very much."