A source told ESPN's Adam Schefter that Sherman signed a one-year contract.
Sherman had been in discussions with the Buccaneers for several weeks and said on "The Richard Sherman Podcast" that multiple teams, including the San Francisco 49ers, Seattle Seahawks and Carolina Panthers, also expressed interest.
"I went with the best offer I had, the best opportunity to go out there and put some great tape on, to lead another group," Sherman said. "I feel comfortable and confident in my abilities to go out there and execute and help that team win."
Sherman said quarterback Tom Brady reached out to him as well.
"He's the all-time great quarterback reaching out, and anytime he makes that call, it's a very difficult opportunity to pass up," Sherman said.
Sherman told reporters later Wednesday that he would need a week to prepare and feel comfortable in the Buccaneers' scheme. Coach Bruce Arians said multiple players would have to be injured for Sherman to play against the New England Patriots on Sunday.
Also Wednesday, the Buccaneers placed wide receiver Scotty Miller on injured reserve. A source told Schefter on Monday that Miller was dealing with a toe injury.
The Buccaneers will be Sherman's third NFL team, after he spent the past three seasons with the 49ers and played the first seven years of his career in Seattle.
Sherman, 33, can provide valuable experience in one of the league's youngest defensive backfields. He is also a sure tackler, which has been an issue for the Tampa Bay defense this season.
The Buccaneers are without Sean Murphy-Bunting, who was placed on injured reserve with a dislocated right elbow Sept. 20, and Jamel Dean, their third cornerback, who left Sunday's game against the Los Angeles Rams with a knee injury in the first quarter and did not return, though he did practice Wednesday.
Sherman is dealing with legal issues and has a pretrial hearing scheduled for Friday in Washington. He was arrested in July in connection with an incident at the home of his wife's parents in Redmond, Washington, and was charged with five misdemeanors, including two counts of domestic violence -- criminal trespass in the second degree and malicious mischief in the third degree -- as well as resisting arrest, driving while under the influence and reckless endangerment of roadway workers.
He pleaded not guilty to all five charges and said in a statement on Twitter in July that he was "deeply remorseful" for his actions and "behaved in a manner I'm not proud of."
In February, King County prosecutors and the sheriff also obtained an "extreme risk protection order'' for Sherman, barring him from having guns after a judge determined he posed a danger to himself and others. Details of the case were sealed.
The Buccaneers did their due diligence on Sherman's legal situation and believe he has the necessary support systems in place, sources told ESPN's Jenna Laine.