Thomas gained 1,062 yards from scrimmage -- including a team-leading 549 rushing yards -- and scored five touchdowns last season, his seventh with the Saints.
The 29-year-old Thomas also caught 77 passes for 513 yards. He missed both of New Orleans' playoff games with a chest injury.
The Saints brought back Thomas one day after adding free-agent safety Jairus Byrd, who agreed to a six-year deal worth $54 million, sources told ESPN.
New Orleans also is attempting to trade veteran running back Darren Sproles, a source told ESPN. Sproles, who has one year left on his contract and is due $3.5 million in salary and bonuses, has drawn heavy interest from other teams, according to the source.
The Saints have been cutting ties with several veterans this offseason, both to shed salary-cap space and invest in younger players. They also released receiver Lance Moore, defensive end Will Smith, linebacker Jonathan Vilma, safety Roman Harper and cornerback Jabari Greer.
ESPN NFL Insider Adam Schefter and ESPN.com Saints reporter Mike Triplett contributed to this report.
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