The 51-year-old Koc, who won over 75 percent of the votes, is a member of Turkey's wealthiest family which runs the conglomerate Koc Holding.
Previous chairman Aziz Yildirim had led the club since 1998.
Fenerbahce, the second most successful club in Turkey, were runners-up in the Turkish Cup this year and will go into the next season's Champions League playoff rounds.
(Writing by Ezgi Erkoyun, editing by Ed Osmond)
