The Nigeria international, who had a loan spell in the Premier League with QPR in the second half of the 2011-12 season, opted to join the Turkish side instead of the Bluebirds
Taiwo, who spent last season on loan at Dynamo Kiev and had a spell at QPR in 2012, opted to leave San Siro due to a lack of first-team opportunities.
|6/4||Cardiff are 6/4 with BetVictor to be relegated next season
"I am delighted. I wanted to play in the Turkish league with a good team and I made a good choice," Taiwo is quoted as saying by Sky Sports.
"Cardiff contacted my agent but I decided to come here."
Former Marseille defender Taiwo made 31 appearances for Dynamo last term, but could not guide them to success as they finished third in their domestic league behind Shakhtar Donetsk and Metalist Kharkiv.
Bursaspor will feature in the Champions League qualifying rounds next season after the expulsion of both Fenerbahce and Besiktas from European competition for match fixing.