The Turkish international's contract has been cancelled by the club after enduring a difficult campaign
The Turkish striker had been expected to leave the club this summer following a disappointing campaign in which the 31-year-old failed to score in 17 appearances.
"Besiktas and Nihat Kahveci have come to a mutual agreement to terminate the player's contract," a statement on the club's official website confirmed.
Last month the striker clashed with team-mate Ricardo Quaresma and a journalist following the club's 1-1 draw with Konyaspor.
Nihat later told Turkish media: "I don't want to play in Turkey anymore."
The player's next destination is currently unknown although interest in Nihat is likely to be strong. Nihat joined Besiktas in the summer of 2009 from La Liga club Villarreal where he spent an injury-hit three years.