The former Tottenham Hotspur and Republic of Ireland striker took charge of the Hungarian side in January 2025 after replacing Pascal Jansen.
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Keane guided Ferencvaros to the league title in his first season and also lifted the Magyar Kupa this term following a 1-0 victory over Zalaegerszeg earlier this month.
However, the club narrowly missed out on retaining the league crown, finishing one point behind champions Gyori ETO.
His departure has already intensified speculation linking him with the managerial role at Celtic, where he previously enjoyed a successful loan spell as a player in 2010.