The Black Sea based side released a statement on the stock exchange disclosing the details of the one-year deal.
Marin will receive a €1.6 million salary in addition to a €10,000 per-match bonus and Trabzonspor have the option to a €4 million buyout clause.
HaberTürk report that Chelsea will pay Marin an additional €900,000 towards his salary and that Trabzonspor managed to negotiate his buyout clause from €7 million down to €4 million.
Marin had his first training session with his new side yesterday after passing his medical.
The 26-year-old has spent the last three seasons out on loan at Sevilla, Fiorentina and Anderlecht since joining Chelsea from Werder Bremen in 2012.
The Germany international will be available to play in the Black Sea Storms next league game against Akhisar.