Levitre earlier hinted at the deal on social media by tweeting "#RiseUp," which the Falcons have been using as a slogan.
Tennessee, which signed Levitre to a six-year, $46.8 million contract in 2013, will receive from the Falcons a sixth-round pick in the 2016 draft and a conditional pick in a future year.
Levitre was moved out of the Titans' starting lineup after the first preseason game, replaced by Byron Bell. The Titans played Bell and then undrafted rookie Josue Matias, skipping past Levitre, during their 24-17 victory over Minnesota on Thursday night in the preseason finale.
The Titans have gotten bigger along the offensive line, and Levitre's poor production and lighter frame -- he's 6-foot-2, 303 pounds -- prompted the team to move on.
Levitre collected a $10.5 million signing bonus when he jumped from Buffalo to Tennessee; he had a total of $13 million guaranteed and was due a base salary of $6.5 million this year.