Crawford, 31, joins linebacker Vic Beasley in heading to the Titans from the Falcons this offseason. Crawford played in all 16 games last season for Atlanta, with four starts.
A fifth-round draft pick for the Raiders out of Penn State in 2012, Crawford, who also played for the Dallas Cowboys, had his best season in 2018 in Atlanta. He had 35 tackles and six sacks that year, making the most of his 11 starts.
The Titans agreed with Beasley on March 17. He signed a one-year, $9.5 million deal, a source confirmed to ESPN.
Crawford's deal comes just hours after Atlanta lost another defensive lineman in free agency. Earlier Tuesday, the Cleveland Browns signed veteran defensive end Adrian Clayborn, who played in 15 games and recorded four sacks for the Falcons in 2019.