Jost, 23, was a restricted free agent. He had seven goals and 17 points in 56 games last season.
"Tyson took a big step last year and was a key contributor to our team. He has worked hard to improve his game and earn a spot in our lineup," said Avalanche general manager Joe Sakic in a statement. "Tyson is a guy with a lot of character who competes at a high level day in and day out. We are excited to have him under contract for another two seasons."