More than $30 million will be guaranteed for Butler, who had two memorable Super Bowl moments while with the New England Patriots.
Deals cannot be officially signed until Wednesday afternoon.
Butler made a game-winning interception in the closing seconds of the victory over the Seattle Seahawks in Super Bowl XLIX following the 2014 season.
Butler was benched for all of Super Bowl LII this past season despite starting 15 regular-season games and both previous playoff games.
Over the past three seasons, Butler started 47 of 48 regular-season games for New England and seven of eight postseason games. He intercepted eight passes in that three-year span and was selected to the Pro Bowl in 2015.
Now he reportedly will join another former Patriots player, Mike Vrabel, who is the new head coach of the Titans.