The deal is worth up to $10 million, a source told ESPN's Adam Schefter.
Clowney will have an opportunity to thrive playing opposite fellow former No. 1 overall pick Myles Garrett.
"I've been getting double-teamed an awful lot in this league, in my career," Clowney said during his virtual news conference. "I'm looking forward to playing with somebody dominant on the other side in Myles Garrett who can draw a double-team. Maybe I can go one-on-one more."
The 28-year-old Clowney visited with the Browns last month, sources told ESPN, but left Cleveland without a deal. General manager Andrew Berry also heavily pursued him last season to pair with Garrett, but the three-time Pro Bowler reportedly rejected Cleveland's multiyear contract offer and ultimately signed a one-year, $13 million deal with the Tennessee Titans.
"We're excited to add Jadeveon to our defensive line," Browns coach Kevin Stefanski said in a statement. "He's a disruptive force that will help us against the run and the pass. We've been able to make some nice additions to our defense throughout free agency and we are looking forward to getting to work, so we can improve our team."
Clowney struggled in 2020 with Tennessee, finishing with 19 tackles and zero sacks in eight games before suffering a season-ending knee injury in November. He had surgery in December and is expected to be at full health for the start of the 2021 season.
"I feel great now," Clowney said. "I'm looking forward to this season to prove to guys that I'm back healthy and I can still dominate in this league."
Over the past three seasons, Clowney has ranked fifth in the NFL with a pass rush win rate of 25%, according to ESPN Stats & Information. During that span, Garrett ranks third, at 26%.
"We love his relentless style of play," Berry said in a statement. "He's one of the more disruptive players in the game and we think he's going to add an element of ruggedness along our defensive line and will pair nicely with many of the guys we have on the roster already. The other thing we love about Jadeveon is his versatility, his ability to play all across the front and impact the game regardless of his alignment."
Cleveland already bolstered its pass rush in free agency last month, signing Takk McKinley to a one-year deal. McKinley struggled with injuries last season but ranked seventh in pass rush win rate in 2018, one spot behind Clowney and four behind Garrett that season.
The No. 1 overall selection by the Houston Texans in 2014, Clowney can play any position along the defensive front, which makes him valuable to teams wanting scheme versatility. He is a disruptive player as an interior pass-rusher or coming off the edge.
Clowney has 255 tackles (75 for a loss), 86 quarterback hits and 32 sacks in his seven seasons. Over his career, he has dealt with various knee injuries in addition to groin, elbow, back and Lisfranc injuries.
The Browns now have three of the past seven No. 1 overall draft picks on their roster, including quarterback Baker Mayfield.
ESPN's Jake Trotter and Turron Davenport contributed to this report.