The 35-year-old joined the Turkish giants in July 2017 after leaving Real Madrid on a free transfer and he made 23 appearances in his only full season.
He had continued to feature regularly this term, turning out 10 times in the Super Lig, with his final game coming against Sivasspor on November 11.
But, with the club in financial difficulty and reportedly trying to cut their wage bill, Pepe's departure has been hinted at for several weeks and he bade farewell to supporters at Sunday's 2-2 draw with Trabzonspor.
And on Monday, Besiktas confirmed via a statement: "Besiktas and Kepler Laveran Lima Ferreira Pepe have mutually cancelled their contract and parted ways. The club thanked the Portuguese star for his efforts and wished him luck in his future career."
There are reports Pepe paid the wages of several members of club staff before the termination of his contract, which was said to be worth roughly €9.5million before bonuses.
Further speculation has suggested the experienced centre-back had been hoping to return to Portugal to see out the remainder of his career.
Porto has already been linked with bringing him back to Estadio do Dragao, with Pepe having last played for them in 2007.