The Germany international has joined the Turkish Super Lig side on a year long loan, the agreement includes an option to purchase.
Marin spent the past season on loan at Fiorentina and Anderlecht.
The Chelsea winger arrived at Trabzon airport on a private jet earlier this week and was greeted by Trabzonspor fans who presented the 26-year-old with a team scarf.
Marin will become the second former Chelsea player at Trabzonspor following the transfer of Jose Bosingwa.
Former Blues players Samuel Eto’o, Gökhan Töre, Raul Meireles and Ricardo Quaresma also play in the league while Kenneth Omeruo is on loan from Chelsea at Kasımpaşa.
Trabzonspor have won both league games this season and take on Akhisar next at the Avni Aker.