Bryant's contract is worth $28 million, a source told ESPN.com's John Clayton. With incentives, he could make as much as $29 million.
Cincinnati's addition of Bryant considerably lessens the possibility that the Bengals will sign unrestricted free agent Terrell Owens. A league source told Schefter that the Bengals never made Owens a contract offer.
Receiver Chad Ochocinco has been lobbying for the Bengals to sign Owens since the end of last season, when the Bengals' passing game lacked a deep threat.
"There's always been the speculation and perception out there [about coming to Cincinnati] and Chad kick-started it and lobbied to have me here as a teammate and I welcome it with open arms," Owens, who made a visit to the Bengals, told the Cincinnati Enquirer.
Bryant had career highs with 83 catches for 1,248 yards and seven touchdowns in 2008 with Tampa Bay. He needed surgery for torn cartilage in his left knee during training camp last year, and was bothered by pain in the knee all season. He finished with 39 catches for 600 yards and four touchdowns.
Cincinnati needs at least one proven receiver after releasing Laveranues Coles, who lasted only one season with the Bengals. Receiver Matt Jones, who was out of the NFL last season after Jacksonville released him because of off-field issues, has signed a one-year deal with the Bengals.
The Bengals went 10-6 and won the AFC North last season by relying on their defense and running game. They lost to the New York Jets in their first playoff game since 2005, struggling to move the ball.
Owens, a six-time Pro Bowl receiver, had 69 catches for 1,052 yards and 10 touchdowns with Dallas in 2008, and dropped off to 55 catches for 829 yards with five touchdowns last season in Buffalo.
Cincinnati's passing offense finished 26th in the league last season even though quarterback Carson Palmer was back from an elbow injury. The Bengals didn't have a reliable third-down receiver -- T.J. Houshmandzadeh left as a free agent for Seattle before last season -- and Coles failed to blend into the offense.
The Bengals also lacked a deep threat after Chris Henry got hurt. Henry later died in a fall from a truck during a domestic dispute.
Getting a receiver and a tight end are among the team's top priorities in free agency and the draft.
Information from The Associated Press was used in this report.