Brown can become an unrestricted free agent next summer.
The Nets also agreed to a one-year deal with free agent James Johnson, his agent, Mark Bartelstein of Priority Sports, told Wojnarowski.
A second-round pick acquired in a deal with the Detroit Pistons before last season, Brown played a crucial role for the star-studded Nets as someone who helped fill in all the gaps.
Brown, who turns 25 later this month, is listed as a 6-foot-4 guard but started 37 games at small forward and was frequently used as a screen-and-roller on offense.
Brown thrived in this role, averaging 8.8 points, 5.4 rebounds and 1.6 assists while shooting 55.6% from the field.