Sanchez led the Jets to two AFC championship game appearances in his first two seasons at the club after being selected sixth overall in the 2009 Draft.
Head coach Rex Ryan told the club's official website: "I'd like to thank Mark for everything he's done for this team and me personally.
"We were rookies together and had some early success, becoming the first rookie head coach and quarterback to go to back-to-back championship games.
"We experienced a lot together and I really appreciate Mark. He's a great player, a great teammate, and I wish him nothing but the best."