Mills, who had declined his $6.2 million option earlier this week, opted to return as NBA free agency opened Thursday, agreeing to a two-year, $14.5 million deal, his agent, Steven Heumann of CAA Basketball, told ESPN's Adrian Wojnarowski.
Claxton, meanwhile, agreed on a two-year, $20 million deal with the team, sources told Wojnarowski.
Mills, 33, joined the Nets last season after playing the past 10 years with the San Antonio Spurs.
One of the league's premier sharpshooters, Mills stepped up for the Nets in the absence of the injured Joe Harris, starting 48 games for Brooklyn. He came off the bench in their first-round loss to the Boston Celtics, playing 18 minutes per game in the series.
Mills had another strong shooting campaign, canning 40% of his 3-pointers on 7 attempts per game in the regular season. Despite never playing starter minutes, Mills has made more than 1,000 3s over the past six seasons. He is the only player in the NBA to hit that many 3-points while playing under 30 minutes per game each season during that span.
Mills hit a career-high 227 3-pointers last season.
Mills is also a highly respected teammate, having won the NBA's Joe Dumars Trophy last season for best representing the ideals of sportsmanship on the court.
Claxton, 23, quickly worked his way into the Nets' rotation as a second-round pick in the 2018 draft, giving a top-heavy Brooklyn team some much-needed defense off the bench.
The 6-foot-11, 215-pound center showed flashes as a switch defender who can guard out on the perimeter and protect the rim. His offense, however, was limited to finishes around the rim.
Claxton averaged 8.7 points and 1.1 blocks per game while playing a career-high 20.7 minutes per game.