Traore, 25, returns to the Premier League following three seasons in France.
"We're delighted that Bertrand has chosen to come to Villa," Villa manager Dean Smith said.
"He's a player with immense talent who will really enhance our attacking options."
Traore is Villa's fourth major summer signing, following the arrival of goalkeeper Emiliano Martinez from Arsenal, striker Ollie Watkins from Brentford and right-back Matty Cash from Nottingham Forest.
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