The Cameroon international has put pen to paper on a three-and-a-half-year contract after passing a medical.
But Makoun will not be eligible to play for up to two weeks while he obtains a work permit.
The 27-year-old becomes Villa boss Gerard Houllier's first major signing since replacing Martin O'Neill in September.
Houllier had also unsuccessfully tried to sign Makoun from Lille when he was in charge of Lyon.
His arrival will provide competition for Villa skipper Stiliyan Petrov and Nigel Reo-Coker.
Houllier said: "Jean is a player who can play in front of the defence as a sitter and defensive midfielder or as a box-to-box midfielder. He has several assets about his game. He is also a very experienced player because he played Champions League football with Lille and Lyon.
Makoun said: "I am thrilled to be here at Aston Villa. I am really, really happy and very proud to have joined a great club.
"Villa have been after me for quite a while, so I am delighted it's finally happened. I can't wait to get started now.
"I've left a very good club in Lyon, a side which has played Champions League football, but I am very excited by this new challenge at Aston Villa. Villa really want to do well and really want to achieve something, so I am really excited to be joining."
Source: PA
Source: PA