The contract is for one year and is worth $8 million, reports ESPN's Adam Schefter.
Suh played the 2019 season on a one-year, $9.25-million deal, joining Tampa on the heels of a one-year stint with the Los Angeles Rams. He helped the Buccaneers field the league's top-ranked defense against the run, finishing the year with 41 tackles.
Incidentally, Suh played against Brady in Super Bowl LIII while with the Rams. The two also battled for years in the AFC East when Suh was with the Miami Dolphins and Brady was a member of the New England Patriots.
Suh, 33, will be embarking on his 11th NFL campaign. The former No. 2 overall pick has 58.5 career sacks, though most of them came in the first half of his career. He has never missed a game due to injury.