Sources told ESPN that the deal is worth $16.5 million (including incentives).
"Brent is the kind of playmaking defensive back that will make an immediate impact in our secondary," Bucs GM Jason Licht said in a statement Friday. "[He] will come in and provide an immediate upgrade at a position we felt we needed to address this offseason. His familiarity with our defensive system, combined with his aggressive style of play, makes him an ideal fit for us."
Grimes, who was a Pro Bowl selection for all three of his seasons in Miami while totaling 13 interceptions, was released by the Dolphins as they had to make room on the roster after a blockbuster trade with the Philadelphia Eagles on Wednesday.
Grimes, who was scheduled to make $8 million in 2016, recorded 49 tackles and four interceptions last season.
While Grimes was a Pro Bowl selection on the field, his wife, Miko, made headlines off it.
Miko Grimes, who hosts a Miami radio show, has publicly criticized Dolphins quarterback Ryan Tannehill, used Twitter to object to topics like her husband not winning MVP honors at the Pro Bowl, his alleged mistreatment by the Atlanta Falcons, what she sees as the NFL's greed and sexism and her unhappiness with the New England Patriots for parting company with defensive lineman Vince Wilfork.
She was also arrested on charges of battery on a police officer, resisting arrest and disorderly conduct outside of Sun Life Stadium before a Bills-Dolphins game in September. The charges were later dropped.
ESPN's Josina Anderson, Ed Werder and James Walker contributed to this report.