The resignation came a day after a meeting between Kocaman and club chairman Aziz Yildirim at which they discussed transfer plans for the new season, media reports said.
Fenerbahce, who finished 10 points behind Istanbul rivals Galatasaray in the league, reached the semi-finals of the Europa League this season before losing to runners-up Benfica.
In his three-season spell, Kocaman won a championship and two Turkish Cups.
Kocaman resigned twice before during the two previous seasons but was convinced to continue by the club management.
Yildirim accepted Kocaman's resignation this time, according to sports channel NTV Spor.
There was no official statement from Fenerbahce and the club were not immediately available for comment.