Floyd, 28, worked out for the Ravens in March, but they did not opt to sign him.
He appeared in 11 games with the Vikings last season, catching only 10 passes for 78 yards and no touchdowns.
Floyd spent 4 1/2 seasons with the Cardinals, who made him a first-round pick in 2012. Arizona cut him after Floyd was arrested for DUI in 2016.
Floyd finished the 2016 season with the Patriots, playing two games.
Tate, 30, has played 126 games in nine seasons. He has averaged 9.5 yards on 200 career punt returns and 23.8 yards on 247 kickoff returns with three return touchdowns.
He spent the past two seasons with the Bills after five seasons with the Bengals and two with the Patriots, who drafted him in the third round in 2009.