The deal for Crowell, who spent his first four seasons with the Cleveland Browns, is for three years. Deals cannot be officially signed until Wednesday afternoon.
The 5-foot-11, 225-pound Crowell has not missed a game since entering the NFL as an undrafted free agent out of Alabama State in 2014.
Crowell, 25, started all 16 games in each of the last two seasons for Cleveland, rushing for a career-high 952 yards in 2016 while averaging 4.8 yards per carry and scoring seven touchdowns.
Last season, Crowell found the end zone only twice while rushing for 853 yards on 206 carries. Crowell has not been utilized much in the passing game, although he had 40 receptions in 2016.
The Jets have a major need at running back. Matt Forte announced his retirement last month and Bilal Powell is better suited to the role of third-down back.