Durham caught 38 passes for 490 yards and two touchdowns with the Detroit Lions last season. Graham had 23 catches for 361 yards and two touchdowns for the Buffalo Bills last year. Harris, a former second-round draft pick, has played 31 games for the Houston Texans over the past three years.
The Titans also agreed to terms with six players, who will join the practice squad.
The practice squad additions are running back Antonio Andrews, defensive lineman Chigbo Anunoby, linebacker Brandon Copeland, offensive lineman Justin McCray, offensive tackle Will Poehls and wide receiver Rico Richardson.