Mills has agreed to a two-year, $12 million deal with the Nets, his agent, Steven Heumann of CAA Basketball, told ESPN's Adrian Wojnarowski. The deal includes a player option.
Brown, meanwhile, is signing his one-year qualifying offer of $4.7 million to return to the Nets, his agent, Ty Sullivan of CAA Basketball, told Wojnarowski.
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.
Mills, 32, finished his 10th season with the San Antonio Spurs in 2020-21 after spending his first two NBA seasons in Portland. Since joining the Spurs, Mills has thrived under Gregg Popovich in a bench role and in more recent years as an important veteran presence off the bench.
Mills averaged 10.8 points per game last season. He's been a consistent threat in the past four seasons, averaging 10.5 points during that span.
In 2020-21, Mills hit a career-high 161 3-pointers, and he's hit at least 150 3s in each of the past four years.
The Australian is currently leading his national team at the Tokyo Olympics.
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.
ESPN's Andrew Lopez contributed to this report.