Terms of the four-year contract weren't available, but the contract is worth about $11 million,
with a signing bonus of about $3.5 million, The Detroit News and the Detroit Free Press reported.
Kitna visited the Jets and Lions and was under consideration by the Ravens. He sensed something was going to happen with another team over the weekend when he told the Bengals he would not be returning.
In response, the Bengals brought in Rams quarterback Jamie Martin for a visit.
Kitna's decision could heat up talks between the Redskins and the Jets for Redskins quarterback Patrick Ramsey. The Redskins want to move Ramsey on Tuesday in a trade. Detroit, the Jets and the Dolphins were the teams talking to the Redskins.
However, the Dolphins traded for Daunte Culpepper later Tuesday.
A nine-year veteran, Kitna played the last five seasons for the Cincinnati Bengals after a four-year stint with the Seattle Seahawks. He was the Bengals' starter as recently as 2003, but then was replaced by first-round draft choice Carson Palmer during the following offseason. In the last two seasons, Kitna has played in just seven regular-season games and started only three.
He relieved the injured Palmer in a wild-card playoff game against Pittsburgh in January, after the starter suffered a torn anterior cruciate ligament, but threw a pair of costly second-half interceptions following several solid series in the first half.
Kitna, who had rejected a mid-season offer to extend his contract, made it clear after that playoff game loss to the Steelers that he would test the free agent market and seek a better situation, one where he might be able to compete for the No. 1 job.
Kitna, 33, has appeared in 92 games and started 79 of them. He has completed 1,667 of 2,837 passes for 18,259 yards, with 108 touchdown passes, 104 interceptions and a passer rating of 75.3. His best season was in 2003, when he threw for 3,591 yards and 26 touchdowns. Kitna earned the league's comeback player of the year for his 2003 performance.
His resume includes four seasons in which he passed for 3,000-plus yards and four in which he posted 15 or more touchdown passes.
The former Central Washington star entered the NFL with the Seahawks as an undrafted college free agent in 1996 and spent the entire season on the practice squad. He became the Seattle starter in 1999, held the job for two seasons, then signed with Cincinnati as an unrestricted free agent in 2001.
Last week, the Lions signed former Tampa Bay quarterback Shaun King, who did not play in the league in 2005, to a one-year contract. Besides Joey Harrington and King, the depth chart also includes second-year pro Dan Orlovsky, a fifth-round pick in 2005 who played sparingly as a rookie.
John Clayton is a senior NFL writer for ESPN.com. Senior writer Len Pasquarelli contributed to this report.