Pollard was part of the Super Bowl-winning Baltimore Ravens but was released this month. He told ESPN's Josina Anderson earlier Thursday that he had agreed to a contract and the team announced the move later in the day.
Asked if it was difficult to leave Baltimore, Pollard told ESPN: "Oh wow, I can't say enough about Baltimore. They were great to me and my family. I will cherish that experience and the relationships I built with the people there for the rest of my life."
The 28-year-old Pollard signed a three-year extension with Baltimore last season, but his release saved the Ravens an estimated $1 million against the salary cap.
Pollard played two years with Baltimore. Last season, he had 71 tackles and an interception despite playing much of the year with six broken ribs.
"Pollard is big, physical, experienced safety. He was a key contributor for the Super Bowl winners last year and his physicality and experience will help us," Titans general manager Ruston Webster said in a statement. "Adding him and George Wilson to our safety group gives us options moving forward and greatly improves our depth there."
Information from ESPN's Josina Anderson, ESPN.com AFC North blogger Jamison Hensley and The Associated Press was used in this report.