A league source told ESPN's Adam Schefter that it's a one-year deal.
Montgomery also has experience as a kickoff returner, another need for the Jets, who hosted the free agent this week on a visit. He also drew interest from the Miami Dolphins.
Jets coach Adam Gase has spoken highly of backup Elijah McGuire, but he evidently wanted a more experienced player behind Bell, the team's marquee addition in free agency.
Montgomery, 26, was traded Oct. 30 to the Ravens, two days after an ill-advised kickoff return contributed to a Green Bay Packers loss to the Los Angeles Rams. He was told to take a knee, but Montgomery took the ball out of the end zone and fumbled, and the Rams held on for the win.
In six games for the Ravens, Montgomery rushed for 83 yards on 15 carries, with no touchdowns. He also caught 10 passes for 65 yards.
Montgomery, a third-round pick in 2015, began his career as a wide receiver, but he switched to running back in 2016. He averaged 5.9 yards per carry that year for the Packers -- 457 yards on 77 carries. He also caught a career-high 44 passes for 348 yards in 2016.