The deal cannot be made official until the new league year begins at 4 p.m. ET Wednesday.
The addition of Watson addresses a position that Ravens officials described as a priority at the NFL combine last month. Crockett Gillmore had offseason surgery on both shoulders and Nick Boyle was suspended last month for the first 10 games of the 2016 season after violating the league's policy on performance-enhancing drugs.
General manager Ozzie Newsome recently suggested that Gillmore is questionable for the start of training camp. Gillmore led all Ravens tight ends in receptions (33), yards receiving (412) and touchdown catches (four) last season.
The Ravens used a second-round pick on tight end Maxx Williams last year, but he had trouble staying healthy throughout his rookie season. Dennis Pitta, who hasn't played since September 2014 because of hip surgeries, could be a post-June 1 cut.
Watson, 35, had a career year on and off the field in 2015. He either set or matched career bests with 74 catches, 825 yards and six touchdowns after replacing Jimmy Graham as the Saints' top tight end.
Watson was also named one of three finalists for the NFL's Walter Payton Man of the Year award after becoming a nationally recognized voice on the issue of race in society and writing his first book, "Under Our Skin."
A first-round pick by New England in 2004, Watson has 4,963 receiving yards and 38 touchdowns in a 12-year career spent with the Patriots, Cleveland Browns and Saints.
The 6-foot-3, 255-pounder has always been lauded for his versatility as a strong blocker and pass-catcher. Because of that versatility, Watson played roughly 85 percent of the Saints' snaps last season.
Watson, who became a valued team leader during his three years in New Orleans, was also elected a team captain last season for the first time in his career. And he is a member of the NFL Players Association's executive committee.
ESPN Saints reporter Mike Triplett contributed to this report.