The team later made the announcement official.
A vocal member of the NFL Players Association, Brees has previously pushed for maximum contract value and told Triplett he would be "lying" to say it wasn't hard to raise the bar contractually for his fellow players -- and his agent, Tom Condon.
"But for me," Brees said, "this was about putting our team in the best position to go win a championship in the next few years."
The annual average for Brees falls short of Jimmy Garoppolo's $27.5 million per year from the 49ers, but the 39-year-old New Orleans veteran exits with a respectable pact. Brees is worth every penny, showing no signs of decline last season while completing 72.0 percent of his passes and posting a 103.9 rating.
For the Saints, urgency existed to reach an agreement before Wednesday's start of the league year when Brees would count $18 million against the salary cap minus a new contract. Rapoport last month suggested Brees would net between $20 million and $25 million annually, leaving the passer on the high end of that spectrum.
A franchise centerpiece since 2006, Brees will remain in New Orleans through 2019. There was never any true doubt about where he would wind up, but putting to bed any Brees-related drama allows the Saints to address other needs.