The 43-year-old Brady, who said he plans to return for the 2021 season, was named Super Bowl MVP for the fifth time.
He also broke his own record for oldest player to win a Super Bowl and joined Pro Football Hall of Famer Peyton Manning as the only quarterbacks to win a title with multiple franchises.
Brady, who won six Super Bowls over 20 seasons with the New England Patriots, completed 21 of 29 passes for 201 yards and three touchdowns against the Chiefs at Raymond James Stadium in Tampa, Fla. The Buccaneers were the first team to play the championship game at home.
"I'm so proud of all these guys," Brady said. "The team had a lot of confidence and we came together at the right time. We ended up playing our best game of the year.
"This team is world champions forever. And you can't take it away from us."
Brady's triumph in his first year with his new team was the Buccaneers' first Super Bowl win since the 2002-03 season, when Tampa Bay defeated the then-Oakland Raiders 48-21. Before this season, the Bucs' last playoff appearance came in the 2007-08 campaign.
The Buccaneers' win prevented the Chiefs from becoming the first back-to-back champions since Brady and the Patriots did it in 2003 and 2004.
Brady's former Patriots teammate and tight end Rob Gronkowski hauled in a team-best six passes for 67 yards and two receiving scores. Leonard Fournette had 16 carries for 89 yards and a rushing touchdown.
Buccaneers defensive coordinator Todd Bowles and his defense helped Brady earn the Vince Lombardi Trophy. Bowles devised a plan that limited quarterback Patrick Mahomes and the Chiefs for most of the game.
Mahomes, almost always under pressure, was 26 of 49 passing for 270 yards and two interceptions. He added five carries for a team-high 33 yards.
Both offenses had sluggish starts, but the Buccaneers eventually got into a groove late in the first quarter. After a 49-yard field goal by Chiefs kicker Harrison Butker, Brady put the Bucs ahead 7-3 with an 8-yard touchdown pass to Gronkowski with 37 seconds left in the opening quarter.
It was Brady's first time scoring a touchdown in the opening quarter of a Super Bowl in his career. Sunday's game was Brady's 10th Super Bowl appearance.
The Buccaneers boosted their lead to 14-3 after Brady found Gronkowski for another touchdown midway through the second quarter. Kansas City responded with Butker's 34-yard field goal after a long drive stalled in the red zone, making it 14-6 with 1:04 remaining before halftime.
Tampa Bay then used two pass interference calls on the Chiefs to set up Brady's 1-yard touchdown pass to receiver Antonio Brown with six seconds left in the opening half, giving the Buccaneers a 21-6 lead at the break.
Mahomes and the Chiefs received the opening kickoff in the second half, but the team again failed to find the end zone when entering Buccaneers territory. Kansas City settled for a 52-yard field goal, bringing the Chiefs' deficit to 21-9.
The Buccaneers answered quickly with a 74-yard scoring drive, capped by Fournette's 27-yard touchdown run. Holding a 28-9 lead, Bucs defensive back Antoine Winfield Jr. picked off Mahomes on the ensuing drive to set up Ryan Succop's 52-yard field goal.
Succop converted the long kick to boost the Buccaneers' advantage to 31-9 near the end of the third quarter. The Buccaneers' defense held Mahomes and the Chiefs to zero points in the final frame, sealing the championship victory with an interception.