Like all deals agreed since Monday, Durant's extension will become official on Saturday after the end of the NBA's free agency moratorium.
The contract was reported hours before Durant and the rest of Team USA play France for the Olympic gold medal in Japan.
Durant, 32, averaged 26.9 points, 7.1 rebounds and 5.6 assists in 2020-21 in his first season back from a ruptured Achilles tendon.
A former league MVP and two-time Finals MVP, Durant played just 35 games last season as the Nets cautiously handled a series of minor injuries.
In the postseason, however, he played in all 12 of Brooklyn's games, including all 53 minutes in the Nets' second-round, Game 7 loss to the Milwaukee Bucks.
Durant scored 34.3 points per game in the playoffs while shooting 51.4 percent from the field and 40.2 percent from three-point range.
The extension is the first for the Nets' trio of superstars, with new contracts expected to come for James Harden and Kyrie Irving.
Brooklyn are the bookmakers' favourite to win the 2022 NBA title, which would be the first in franchise history for the Nets.