The Steelers' backup quarterback in 2008, Leftwich also had a two-year offer on the table to stay in Pittsburgh as Ben Roethlisberger's backup. He had also visited the Washington Redskins last week.
The 29-year-old Leftwich appeared in five games with the Steelers in 2008 after joining the team as a free agent in training camp after Charlie Batch suffered a broken clavicle in Pittsburgh's first preseason game.
He passed for 303 yards and two touchdowns in limited action.
A former first-round pick of Jacksonville, the 29-year-old Leftwich spent four seasons with the Jaguars before losing his starting job in 2006 to David Garrard after suffering an ankle injury.
He appeared in three games for Atlanta in 2007 before signing with the Steelers in 2008.
Of that group, Leftwich has the most starting experience.
The Steelers made a contract offer to Leftwich late last week before he left for Tampa. Currently, the only two quarterbacks Pittsburgh has on its roster are Roethlisberger and second-year player Dennis Dixon, who has never taken an NFL snap.
The loss of Leftwich means the Steelers will likely make a concerted effort to sign Batch, who is also an unrestricted free agent, before the NFL draft, which will be held April 25 and 26.
Meanwhile, KDKA-TV reports that the Steelers may be close to an agreement on a contract extension with linebacker James Harrison that will pay him $48 million.
The deal would make Harrison, the team's MVP the past two seasons, the highest-paid defensive player in team history.
The Steelers have been attempting to reach an extension with Harrison, who's due to earn $1.4 million in 2009, for more than two months.