The three-year deal is worth $30 million, according to multiple reports.
Titans general manager Jon Robinson was director of college scouting in New England from 2008 to 2013, when the Patriots drafted Ryan in the third round out of Rutgers.
Ryan, entering his fifth NFL season, led the Patriots in tackles (92) during the 2016 regular season while rotating between the Nos. 2 and 3 spots on the team's depth chart. While being the leading tackler as a cornerback might not be viewed as a positive, in Ryan's case it is more reflective of his excellent tackling and run-force skills that Patriots coaches valued highly.
Ryan hasn't missed a game in his NFL career, which is the type of durability that increased his value as a free agent. The 5-foot-11, 195-pound Ryan also has the flexibility to play inside and outside.
He has 13 career interceptions in the regular season, and one in the postseason. He turned 26 on Feb. 9.
Ryan is represented by Neil Schwartz and Jonathan Feinsod.
ESPN's Mike Reiss contributed to this report.