All first-round contracts include a team option for the fifth year.
The defensive end was a three-year starter at Texas A&M, where he had 31 sacks, 141 tackles and seven forced fumbles.
The former Texas A&M All-American signed his contract Friday and the Browns posted a video of Twitter of Garrett filling out the paperwork while Seal's "Kiss From A Rose" played in the background.
According to NFL Network's Ian Rapoport, Garrett's contract is for four years and worth $30.4 million, with a signing bonus of $20.25 million.
Cleveland is hoping the 6-foot-4, 272-pounder can immediately improve the team's pass rush and provide a dynamic force on the defensive side of the ball under defensive coordinator Gregg Williams. The Browns now have signed six of its picks from April's draft.More news: Deere Announces Earnings for Second Quarter
Garrett caused a stir shortly after being drafted by saying he was targeting Pittsburgh Steelers quarterback Ben Roethlisberger for his first sack. The Browns meet the Steelers in Cleveland in the first game of the 2017 season.
"I think that was kind of blown up, but I stand by it", Garrett said at minicamp. We feel like he's doing the right things to get better.
"You're trying to make a name for yourself. They are not going to shy away from the challenge and neither are we".
In addition to Brantley, the team has signed defensive end Myles Garrett, defensive tackle Larry Ogunjobi, cornerback Howard Wilson, offensive tackle Roderick Johnson, place kicker Zane Gonzalez and running back Matthew Dayes. Physically, you guys have seen him.