Arriving on transfer deadline day, Sylla becomes the first capture of the January transfer window for Villa, who are currently 19th in the Barclays Premier League.
The defensive-minded player passed a medical on Thursday morning and is eligible to make his debut in Saturday's league clash with Everton at Goodison Park.
Sylla, who has represented France at Under-21 level, said: "I'm very excited about the prospect of playing for Aston Villa and also to be playing in the Premier League.
"The manager (Paul Lambert) is building a dynamic and exciting young team here and there are players also with a lot of experience.
"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."