Three-time NFL Most Valuable Player Brady, who turns 43 in August, said Tuesday he was leaving the New England Patriots after 20 seasons with the club under coach Bill Belichick.
Both the NFL's website and TV network reported that Brady has agreed to terms on a deal worth $30 million (27.6 million euros) a season.
No contracts can be signed until the start of free agency for the 2020 season at Wednesday at 4 p.m. (2000 GMT), but there is no guarantee any announcement would come then.
Brady joins a Buccaneers club owned by Manchester United owner Malcolm Glazer, a team that has not reached the NFL playoffs since 2007.
The Bucs, who captured their only Super Bowl title in 2003, boast a powerful offensive attack that ranked third in both total offense and scoring in 2019.
Brady has enjoyed great success in finding tight ends during his days with the Patriots, notably connecting with Rob Gronkowski before his retirement last March after a victory in last year's Super Bowl.
The move will send former Tampa Bay quarterback Jameis Winston, the top pick in the 2015 NFL Draft, into free agency after five years as a starter for the Bucs.
Winston has thrown 88 interceptions compared to 121 touchdowns during his time in Tampa Bay. Last year, he led the NFL with 626 pass attempts and 5,109 passing yards but also tossed an NFL-most 30 interceptions.
With 33 touchdown passes as well, Winstron became the first quarterback in NFL history to throw 30 pickoffs and 30 touchdowns in the same season.
Other moves also set to be confirmed starting Wednesday include Houston's reported trade of star receiver DeAndre Hopkins to Arizona for running back David Johnson.
Drew Brees reportedly will sign a two-year deal worth $50 million to remain the starting quarterback for the New Orleans Saints while his backup, Teddy Bridgewater, reportedly will join the Carolina Panthers in a deal the NFL website says will be for three years at $63 million.