Brate's deal is for six years and $41 million with $18 million guaranteed, while Grimes' deal is for one year and $10 million.
An undrafted free agent out of Harvard, Brate was set to become a restricted free agent in 2018 but instead will be with the club through the 2023 season. His 14 touchdown catches since 2016 are third most among tight ends in the league.
Grimes, a four-time Pro Bowler will who will be 35 this year, battled a shoulder injury in 2017 but still started 13 games, finishing with three interceptions and 11 pass breakups. In 2016, he led the NFL with 24 pass breakups and was arguably the Bucs' best player on defense. He also has served as a mentor for first-round draft pick Vernon Hargreaves, who's now entering his third year.
The Bucs have been adamant about re-signing their own this free-agency period, locking wide receiver Mike Evans into a five-year deal Friday worth $82.5 million.