Arriving on transfer deadline day, Sylla becomes the first new arrival of the January transfer window for Villa, who are currently 19th in the 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 midfielder appeared 21 times in the French second tier this season.
He joined Clermont from SM Caen in 2009.