The development was confirmed by the Buccaneers in a statement on Tuesday.
The Patriots are sending Gronkowski and a seventh-round draft pick to Tampa Bay in exchange for a fourth-round selection.
"Rob Gronkowski is one of the best tight ends in NFL history and he plays the game with the type of passion and desire that sets him apart," Buccaneers general manager Jason Licht said.
"Rob has played his entire career alongside Tom Brady and their accomplishments speak for themselves. Together they have developed the type of chemistry on and off the field that is crucial to success.
"Rob combines elite-level skills as both a receiver and blocker but what really makes him special is the fact that he's a proven winner who brings that championship mindset and work ethic."
Gronkowski retired after helping the Patriots win the Super Bowl following the 2018 season, but had said he could return to football at some point.
Earlier on Tuesday, the 30-year-old had revealed he was "not totally done" with the NFL as rumours over his return continued to gain momentum.
And future Hall of Fame quarterback Brady will now have a familiar target when he takes the field for the Buccaneers this season, having left the Patriots after 20 years.
¯\_(ツ)_/¯ pic.twitter.com/d5bMUpcCLr— Tampa Bay Buccaneers (@Buccaneers) April 22, 2020
Gronkowski, who still has a year left on his contract with the Patriots, told New England he wants to return to football, but only with Brady and the Buccaneers, according to widespread reports. The final year of his deal is worth $10million.
At the time of his retirement, Gronkowski was considered one of the greatest tight ends in NFL history but had been plagued by an ailing back.
A five-time Pro Bowler, Gronkowski’s 79 touchdown receptions are third-most in NFL history by a player in his position.
He recently appeared at WWE's WrestleMania but now joins O.J. Howard and Cameron Brate among Brady's tight end options.