The contract reportedly includes $33 million guaranteed at signing, according to NFL Network's Tom Pelissero.
The Panthers have already granted quarterback Cam Newton and his representatives permission to seek a trade.
Bridgewater spent the last two seasons with the New Orleans Saints, where he served as the backup to Drew Brees. He went 5-0 as a starter during 2019 while Brees was sidelined with a thumb injury.
A former first-round pick of the Minnesota Vikings, Bridgewater's career was temporarily derailed by a devastating knee injury before the 2016 season. He appeared in just one game across 2016 and 2017 and then played the last two seasons on one-year contracts.
Last offseason, Bridgewater turned down an opportunity to start for the Miami Dolphins in favor of a return to New Orleans.
Now, the 27-year-old Bridgewater will join a Carolina team that's apparently committed to a full-scale rebuild under new head coach Matt Rhule. The Panthers parted ways with several veterans in recent weeks, bidding farewell to the likes of Greg Olsen, Mario Addison, and James Bradberry.
In 44 career appearances, Bridgewater has thrown 38 touchdowns against 25 interceptions. He owns a lifetime passer rating of 88.3.