The Black sea club announced their acquisition but refrained from disclosing details of the deal.
Bosingwa had most recently been with Queens Park Rangers, but left the London side by mutual consent following their relegation to the Championship.
Bosingwa, 30, made his name at Porto between 2003 and 2008 before moving to the Premier League with Chelsea, where he stayed for four years, winning the Champions League in 2012.
He spent just one season at QPR, making 23 appearances during the Hoops' doomed campaign.
Trabzonspor finished ninth in the Super Lig last season, but qualified for the Europa League by reaching the final of the Turkish Cup.