Bouma has struggled with injuries and has been unable to recapture the form he first showed when he arrived at Villa Park from PSV Eindhoven in 2005.
The 31-year-old has not figured for the first team since dislocating his ankle against Odense in 2008 with his comeback hampered by a series of niggling injuries.
The Dutchman will not have his contract renewed as he looks to get his career back on track.
Villa boss Martin O'Neill paid tribute to Bouma, who made 90 appearances for Villa, scoring one goal.
"Freddie epitomises the kind of qualities we associate with top Dutch players and he has been really unfortunate to have been sidelined because of injury," O'Neill told the club's official website.
"That came as a real blow because, as a player, I have the utmost regard for him and he has been a totally positive influence at the club throughout my time here.
"He has fought back strongly to get himself fit again and he really wants to get back to the level of which he is undoubtedly still capable, so he wants to take this opportunity to do that and I wish him only the best."