The 30-year-old star forward made his announcement on social media moments after the start of the NBA's free agency period, saying he will sign a maximum-level deal with the Nets.
Durant commands top dollar despite suffering a ruptured Achilles tendon in game five of this year's finals, and is expected to miss all of the 2019-20 season.
"Kevin Durant has confirmed he will sign a max deal with the Brooklyn Nets," said a post on the Instagram and Twitter accounts of The Boardroom, his company-owned sports-business network.
A max deal for Durant would be worth some $164 million over four years. The Warriors could have offered him $221 million over five years to stay.
Under NBA rules, teams cannot sign contracts with players until Saturday, but there was still plenty of action in the opening hours of the free agency period.
Multiple US media outlets reported that Boston Celtics playmaker Kyrie Irving would be joining Durant in Brooklyn on a four-year deal worth $141 million.
It could give the Nets a formidable duo once Durant returns from an upcoming year of rehabilitation, provided Durant can regain the form that helped power the Warriors to the 2017 and 2018 NBA crowns.
Durant had the Warriors looking like champions again this year before a right calf injury sidelined him. He missed nine games before returning in game five of the NBA Finals against Toronto. He scored 11 points in 12 minutes before suffering the ruptured tendon that required surgery two days later.
Durant and Irving were both reported to be targets of the New York Knicks -- who were coming off a league-worst 17-65 season and had cleared salary cap space to sign proven talent to join their inexperienced squad.
The Knicks -- apparently unwilling to offer Durant a maximum deal because of his injury -- were reported to have instead agreed to terms with Julius Randle and Taj Gibson.
Randle, 24, averaged 21.4 points, 8.7 rebounds and 3.1 assists in 73 games with the New Orleans Pelicans last season. Gibson, 34, averaged 10.8 points and 6.5 rebounds in 70 games with the Minnesota Timberwolves.
Walker headed to Boston
With Irving headed out of Boston, the Celtics were poised to welcome point guard Kemba Walker -- a three-time All-Star who is coming off one of the best seasons of his career for the Charlotte Hornets with averages of 25.6 points, 5.9 assists and 4.4 rebounds.
While the Warriors will bid farewell to Durant, three-point sharpshooter Klay Thompson signed a new five-year deal worth $190 million to stay with the club.
And the Warriors will also welcome point guard D'Angelo Russell, set to arrive from Brooklyn on a four-year, $117 million contract, ESPN said, citing league sources.
The future remained unclear for two-time NBA Finals MVP Kawhi Leonard, who led the Raptors to the title after being traded from the San Antonio Spurs, whom he sparked to the 2014 crown.
The Knicks and the Los Angeles Clippers have long been expected to make high-priced pitches to Leonard, who grew up in Los Angeles.
The Los Angeles Lakers are also in the hunt for Leonard, seeking a third star to unite with LeBron James and Anthony Davis, who is set to join the Lakers in a deal with New Orleans.
Leonard could opt to stay with Toronto, and the Raptors reportedly have been assured they will be able to make the final presentation to Leonard after other suitors have made their pitches.
In other reported deals, four-time All-Star Al Horford agreed to a four-year, $97 million contract with the Philadelphia 76ers after three years in Boston.
The Sixers also signed a four-year deal with Jimmy Butler as part of a sign-and-trade agreement that will send Butler to the Miami Heat.
The Dallas Mavericks said they had agreed with restricted free agent Kristaps Porzingis on a five-year, $158.253 million maximum salary contract -- the largest in the 39-year history of the club.
The 23-year-old Latvian was acquired by the Mavericks from the Knicks in a blockbuster seven-player trade on January 31.
He was still recovering from surgery to repair a torn left knee ligament and hasn't played since February 6, 2018.