Tate, 25, spent the first four seasons of his career with the Houston Texans. After sitting out his rookie season in 2010 with a broken ankle, he rushed for a career high 942 yards in 2011, but was hampered by injuries in the next two seasons.
Considered one of the top running backs on the open market, Tate rushed for 771 yards and four touchdowns this past season.
Though the Texans' running game struggled in 2013, Tate tied a franchise record with three rushing touchdowns against New England in Week 13. He took over as the starter in Week 7 in Kansas City, a game during which Tate broke four ribs.
Tate played with the injury for eight games, but said he re-aggravated a previously cracked rib in Week 15 against the Indianapolis Colts. Tate said it didn't make sense for him to continue playing and went on injured reserve.
The Browns have been desperate to find a quality every-down running back since trading Trent Richardson to Indianapolis early last season. Cleveland ranked tied for 27th in the league with 86.4 yards rushing per game last season and scored only four touchdowns on the ground.
ESPN.com Texans reporter Tania Ganguli and The Associated Press contributed to this report.
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