Winston and the Saints agreed to terms on a two-year contract, the team announced Tuesday.
Financial details were not announced but the deal has a base value of $28 million, including $21 million guaranteed, a source told ESPN's Adam Schefter on Monday. Winston can make up to $44 million with incentives, a source told ESPN's Jeremy Fowler.
The Saints were one of four teams vying to acquire Watson, who was ultimately traded to the Cleveland Browns.
Winston, 28, went 5-2 in his first year as a starter with the Saints last season, but he tore the ACL in his left knee and suffered MCL damage on Oct. 31. A league source told Schefter that Winston is expected to be ready for training camp this summer "if everything continues to go smoothly with his rehab."
The former No. 1 overall NFL draft pick and Heisman Trophy winner posted a career-high passer rating of 102.8 with the Saints last season, completing 95 of 161 passes (59%) for 1,170 yards and 14 touchdowns with three interceptions. He also ran for 166 yards and one touchdown and lost one fumble.
Although Winston averaged just 186 passing yards in his six full games, he still flashed his big-play ability with four completions of 49-plus yards. And he proved that he could overcome the turnover issues that plagued him during his first five NFL seasons with the Tampa Bay Buccaneers.
Winston went 28-42 as a starter with the Buccaneers, completing 61.3% of his passes for 19,737 yards and 131 total touchdowns, including 10 rushing. He also had 88 interceptions and 23 lost fumbles.
He displayed some dynamic highs and lows during his tenure with the Bucs -- especially in 2019 when he led the league with 5,109 passing yards while also becoming the first quarterback in NFL history to throw at least 30 touchdown passes and 30 interceptions in the same season (33 TDs and 30 INTs).
When Tampa Bay elected to move on to Tom Brady in 2020, Winston joined the Saints as a backup to try and revive his career under then-coach Sean Payton and starter Drew Brees. Winston signed a one-year deal that was worth just $1.1 million plus incentives because he said he wanted to get a "Harvard education in quarterback school."
Winston signed another one-year deal with the Saints before the 2021 season that included $5.5 million in guarantees and up to $7 million in incentives after Brees retired. He beat out Taysom Hill to win the starting job in the preseason, and he was repeatedly praised by Payton for both his arm strength and his leadership.
ESPN's Mike Triplett contributed to this report.