Burkina Faso international Traore began his senior career with Villa's Premier League rivals Chelsea and has also had loan spells with Dutch clubs Vitesse and Ajax.
The 25-year-old boosts Villa's attacking options further following the arrival of Ollie Watkins from Brentford for a club-record £28million earlier this month.
Details of Traore's contract at Villa Park have not been announced by the club.
Villa boss Dean Smith told his club's website: "We're delighted that Bertrand has chosen to come to Villa.
"He's a player with immense talent who will really enhance our attacking options."
Villa escaped relegation on the final day of last season after winning promotion through the Sky Bet Championship play-offs.
The club, who have also recently signed goalkeeper Emiliano Martinez and full-back Matty Cash, kick off their top-flight campaign at home to Sheffield United on Monday evening.