Watson spent the past six seasons in New England, where he previously worked with Browns coach Eric Mangini and offensive coordinator Brian Daboll.
Watson visited the Browns on Thursday, when the team also hosted quarterback Jake Delhomme and running back Justin Fargas.
Delhomme is scheduled to visit the New Orleans Saints on Friday. While the Super Bowl champions are looking for a backup for Drew Brees, the Browns might see Delhomme as their starter. That prospect could be enough for Cleveland to land the 35-year-old, who was released by the Carolina Panthers last week.
Meanwhile, Watson should improve a position that has been thin for the Browns since they traded Kellen Winslow to the Tampa Bay Buccaneers last offseason. Steve Heiden, an 11-year-veteran who was released later Friday, has been plagued by injuries in recent years and missed the final nine games last season after going on injured reserve. Robert Royal caught just 11 passes and had numerous drops. Evan Moore was a late-season find off the practice squad, but he lacks experience, which is why the Browns were excited to sign Watson.
"We viewed Ben as one of the top all-around tight ends in the free-agent market," Browns general manager Tom Heckert said in a statement released by the team. "Because of his athleticism and intelligence, he has proven valuable as both a receiver and blocker during his career, and has performed well in both facets. He comes from a winning program in New England and possesses the traits that we like in a player.
"We feel as though he can help us in many different areas and we are excited about his addition to our team."
Last season, Watson started all 16 games for the Patriots and caught 29 passes for 404 yards and five touchdowns.
A first-round draft pick by New England in 2004, the 6-foot-3, 255-pounder has made 47 career starts. He has caught 167 passes for 2,102 yards and 20 touchdowns.
Watson had his best season in 2006, when he had 49 receptions for 643 yards and three TDs. His only 100-yard receiving game came against the Browns in 2007.
The Associated Press contributed to this report.