The 30-year-old Frenchman joined the Magpies on a short-term contract in November last year after being released by Paris St Germain.
Fabrice Pancrate: "I am really disappointed not to be a Newcastle player next year. This was the best club that I played for and not to be part of it next year is tough to take.
"The fans were the best I have played in front of and it was a great feeling to play in front of them and in front of so many at the away games.
"I didn't want to leave the club because I loved it."