Last season, Dunn became the 22nd back in NFL history to rush for 10,000 yards. But his days in Atlanta were numbered after the Falcons doled out a six-year contract to Turner.
Turner's contract is worth
$34.5 million with approximately $15 million guaranteed, sources told ESPN.com's Michael Smith.
The 33-year-old Dunn had three straight 1,000-yard seasons with the Falcons, helping the team lead the NFL in rushing from 2004-06. He ran for a career-high 1,416 yards in 2005, earning his third Pro Bowl appearance.
But the 11-year veteran found little room to run after the Falcons fired coach Jim Mora and brought in Bobby Petrino. Dunn rushed for just 720 yards and averaged 3.2 yards per carry during a dismal 4-12 season, which was marred by Michael Vick's dogfighting case and Petrino's sudden resignation 13 games into his debut season.
With a new coach and general manager, the Falcons decided to go for a younger running back, signing Turner to team with 24-year-old Jerious Norwood.
"The legacy he leaves in Atlanta will be long-remembered and appreciated by his fellow players, fans and the community," Atlanta owner Arthur Blank said. "In my mind, Warrick will always be part of the Falcons family."
Within hours of his release from the Falcons, Dunn spent Monday visiting the Tampa Bay Buccaneers to determine whether he might return to the team with which he started his NFL career, agent Jim Steiner told ESPN's Ed Werder.
Dunn, 33, is expected to make numerous visits before making a final decision. In addition to the Bucs, Dunn has drawn interest from the Houston Texans and Tennessee Titans. The Indianapolis Colts remain a possibility because they are coached by Tony Dungy, who drafted Dunn with the Bucs.
Dunn's preference to play for an established winner also makes the Dallas Cowboys a possibility. With Pro Bowler Marion Barber a restricted free agent and 16-game starter Julius Jones and special-teamer Tyson Thompson unrestricted free agents, the Cowboys have no established running backs under contract.
However, the Cowboys would be reluctant to decline their opportunity to match any offer for Barber even for first-and third-round draft choice compensation.
The Cowboys also believe there is depth at running back in the upcoming draft, creating a strong sense in the organization that the team should focus on adding a younger player and perhaps a more physical specimen than the diminutive Dunn.
Team owner and general manager Jerry Jones might consider it difficult to justify using a premium draft choice on a running back if the Cowboys already had both Barber and Dunn on their roster.
Dunn spent six seasons with the Falcons, leaving as the third-leading rusher in franchise history with 5,979 yards. He was also well known for his charitable work, most notably the "Home For The Holidays" program that helped single parents become first-time homeowners by making the down payment on new furnished homes.
In 2004, Dunn received the Walter Payton NFL Man of the Year award.
Dunn's final season with the Falcons was largely forgettable. Vick's legal troubles deprived the team of one of its best running threats, and the offensive line struggled to adapt to Petrino's blocking scheme.
But Dunn did join an exclusive club in Week 12, reaching 10,000 yards in a loss to the Colts. For his career, he has 2,484 carries for 10,179 yards and 47 touchdowns, along with 463 receptions for 4,009 yards and 15 TDs.
"Warrick has performed at an extremely high level for a very long time," Falcons coach Mike Smith said. "Making moves like this one are never easy. It's tough. But we have to do what we feel is in the best long-term interest of the Falcons."
Dunn spent his first five seasons with the Buccaneers, twice rushing for 1,000 yards and earning two trips to the Pro Bowl. He was drafted 12th overall out of Florida State in 1997.
Information from ESPN's Michael Smith and Ed Werder and The Associated Press contributed to this report.