The move comes two days after West was released by the Kansas City Chiefs. West had been sidelined for most of training camp because of a concussion before being cleared for padded practice on Tuesday.
West saw sparse action with the Chiefs last season — his fourth with the club. He was limited to 18 carries for 72 yards and two touchdowns, as rookie Kareem Hunt served as the primary ball carrier.
An undrafted free agent out of Abilene Christian in 2014, West had his best season with Kansas City in 2015. He led the team in rushing with 634 yards and four touchdowns, and added 20 receptions and a score in 15 games, including nine starts.
West rushed for 293 yards and a touchdown in 2016, but he set a career best with 28 receptions — one more than last season — and two more touchdowns.
The 5-foot-10, 205-pound West is one yard shy of 1,000 rushing yards for his career. He has 75 catches for 552 yards in 49 games (11 starts).
West joins a crowded backfield in New York that is headed by Isaiah Crowell, Bilal Powell and Thomas Rawls.
Elijah McGuire, expected to compete for the primary backup job to Crowell, sustained a broken foot during the team’s first training camp practice.