Brees and the team reached the agreement on Friday, which will pay the quarterback $40 million in the first year, the person told The Associated Press on condition of anonymity because the contract had not been publicly announced.
The Saints announced they had reached a five-year deal with Brees but did not release financial details of the contract.
Brees posted a note on his Twitter page reading, "Deal is Done! Love you, Who Dat Nation. See you soon!"
Brees had been tagged as the Saints' exclusive franchise player and could not negotiate with other teams.
Had a deal not been reached, the tender for a quarterback was worth $16.3 million. Brees would have had to play for that amount or hold out for a better one-year deal, which would have left his long-term future in New Orleans uncertain.
Brees skipped the Saints' offseason practices while holding out for his new long-term contract, which now gives him the highest average annual pay ($20 million) in NFL history. Buffalo defensive end Mario Williams also has a $100 million contract, but for six years.
Now Brees is set to report for the opening of Saints training camp on July 24, a needed dose of good news for a club whose offseason has been plagued by the bounty scandal that resulted in the season-long suspensions of head coach Sean Payton and linebacker Jonathan Vilma, among other sanctions.
New Orleans had designated Brees, 33, as its franchise player in March after the club was unable to reach a new long-term extension with the record-setting quarterback before his previous six-year, $60 million contract expired.
Brees, however, was steadfast in not wanting to play for a one-year deal.
During the past six seasons, Brees has not only led the Saints to their only Super Bowl title, but has completed more passes (2,488) for more yards (28,394) and more touchdowns (201) than any other quarterback in the NFL. His 67.8 percent completion rate spanning the past six seasons also tops the league.
In 2011, Brees set NFL single-season records with 468 completions, 5,476 yards passing and a completion percentage of 71.2. His prolific passing numbers helped the Saints set a new NFL high for total offensive yards in a season with 7,474. Brees yards-passing record shattered a mark of 5,084 set by Dan Marino back in 1984.
He led the Saints to a 13-3 regular season record and their second NFC South Division title in three seasons. New Orleans defeated Detroit in the first round of the playoffs before falling in the final seconds of its second-round game at San Francisco.
This offseason marked the first time Brees had the opportunity to negotiate a major, long-term deal with the leverage provided by a string of injury-free seasons highlighted by a slew of individual and team statistical records, in addition to a championship.
He commanded only second-round money when he was drafted by San Diego, and the Chargers placed the one-year franchise tag on him when that deal ran out in 2005. The right-handed Brees then had an injury the following season that required major surgery to his throwing shoulder, and which left him with few major offers during the 2006 offseason.
He wound up signing the six-year deal in New Orleans that left him playing for well below what the top quarterbacks in the league earned during the past few seasons.
Brees' new deal tops the previous benchmark contract for elite QBs set by with the five-year, $96 million deal Denver gave earlier this offseason to Peyton Manning, who is three years older than Brees and sat out last season while recovering from neck surgery.