The Browns have reached an agreement with Bowe on a two-year deal, according to ESPN NFL Insider Adam Schefter. NFL Network first reported the news.
Bowe took to Twitter on Thursday afternoon to express excitement for his "next chapter....Cleveland! Look forward to spending time with the DAWG POUND in the endzone!!"
The Kansas City Chiefs released Bowe after eight seasons with the team.
Bowe visited Cleveland last week and had a productive meeting with the staff. He has a relationship with general manager Ray Farmer, who previously worked in Kansas City's personnel department.
"Dwayne brings a nice combination of size and speed to our wide receiver group," Browns coach Mike Pettine told the team's website Friday. "He is a veteran player that has been productive and caught a ton of footballs in this league. His size and catch radius make him very quarterback-friendly, and we are happy to add him to our team."
Bowe and former Miami Dolphins receiver Brian Hartline add veteran experience to the Browns' pass-catching lineup, but the only receiver on the roster with more than two touchdowns last season is Travis Benjamin (three).
Josh Gordon, whom the Browns suspended for the last game of 2014 and is suspended for all of 2015, welcomed fellow wide receiver Bowe to Cleveland via Twitter.
The Chiefs released Bowe, 30, because of his hefty salary-cap figure and declining production. He failed to live up to the five-year, $56 million contract he signed in 2013 and was scheduled to cost the Chiefs $14 million against their salary cap in 2015. He hasn't caught more than 60 passes or had more than 801 yards in any of the past three seasons. In 2014, he was held without a touchdown for the first time in his career.
In his first five seasons, Bowe topped 1,000 yards three times and missed the mark by 5 yards a fourth time. He led the NFL with 15 touchdown receptions in 2010.
Bowe finished his Chiefs career with 532 receptions for 7,155 yards and 44 touchdowns. He accomplished this despite playing with a collection of mostly journeyman quarterbacks and others who never established themselves in the NFL: Damon Huard, Brodie Croyle, Tyler Thigpen, Matt Cassel, Tyler Palko, Kyle Orton, Brady Quinn, Alex Smith and Chase Daniel.
Bowe's best season was 2011, when he caught 81 passes for 1,159 yards and led the NFL with 15 receiving touchdowns. Since then, his best season totals were 60 catches, 801 yards and five touchdowns, and each of those totals happened in different years.
During his eight seasons with the Chiefs, the NFL suspended Bowe twice: in 2009 for four games for a violation of the league's policy on performance-enhancing drugs, and in 2014 for a game for violation of the league's substance-abuse policy.
Bowe's release saved the Chiefs $5 million against their salary cap.
ESPN.com Chiefs reporter Adam Teicher contributed to this report.