Terms were not disclosed.
Tate averaged 26.1 yards on 35 kickoff returns last season, while also averaging 9.3 yards on 36 punt returns.
The 26-year-old has spent the past three seasons with the Bengals after playing his first two years with New England.
Tate has 38 career receptions, just one last year, for 649 yards in 66 NFL games. He has also averaged 25.1 yards on 154 kickoff returns and 9.8 yards on 109 punt returns.