Brees will receive $27 million guaranteed in the first year, NFL Network's Tom Pelissero reported. The contract is expected to be finalized later on Tuesday.
Had the 39-year-old Brees remained unsigned by Wednesday, $18 million in dead money from his current contract would immediately count against the team's salary cap in 2018.
Brees set an NFL record for completion percentage (72.0) last season despite throwing for his fewest yards (4,334), touchdowns (23) and interceptions (eight) in his 12 seasons with the Saints.
His short-term contract extension is his second with New Orleans after he signed a one-year, $24.25 million extension before the start of the 2016 season.
A former Super Bowl MVP and 11-time Pro Bowl selection, Brees needs 1,496 yards to break Peyton Manning's record of 71,940. He needs 52 more touchdown passes to break Manning's NFL record of 539.
Brees has thrown for 70,445 yards with 488 touchdown passes and 228 interceptions in 248 career contests since being made a second-round selection in the 2001 NFL Draft by the then-San Diego Chargers.