Montgomery has played both running back and receiver, giving Sean Payton yet another toy for his offense.
The Packers made Montgomery a third-round choice in 2015. He started his career at receiver before moving to running back after the Packers had injuries at the position.
He also returned kickoffs, and in fact, a fumble on a kickoff late in a 2018 game against the Rams, and the aftermath of whether he was told to down it in the end zone, got him traded to the Ravens.
Montgomery, 27, played with the Jets last season, seeing action in 16 games with two starts.
He had 45 touches for 193 yards and returned 18 kickoffs for a 20.2 yards average last season.