Bridgewater appeared to confirm the news with a post on social media.
Sources informed the NFL Network on Tuesday that Bridgewater was expected to sign with the Saints. The quarterback elected to visit with the Dolphins on Wednesday but left Miami without a deal.
Bridgewater is viewed as the potential successor to veteran quarterback Drew Brees. He started only one game with the Saints last season, but sat behind Brees and learned head coach Sean Payton's scheme.
Bridgewater has a 17-12 record as a starter and was selected to the Pro Bowl in 2015. He has completed 565-of-874 passing attempts for 6,268 yards and 29 touchdowns.