The Nuggets also agreed to a two-year, $10 million deal with 13-year veteran Jeff Green, his agent Jason Glushon told ESPN's Malika Andrews. The agreement includes a player option in the second year of Green's contract.
In addition, Denver reached a two-year agreement to keep forward JaMychal Green, according to multiple reports. His deal is for $17 million.
Re-signing Barton, whose seven seasons in Denver make him the longest-tenured Nugget, was considered a top priority for president of basketball operations Tim Connelly. Barton, 30, declined his $14.7 million player option for next season, making him a free agent.
The veteran wing suffered a hamstring injury and missed more than six weeks at the end of the regular season and into the playoffs before returning for Game 2 of the Western Conference semifinals against the Phoenix Suns. He averaged 12.7 points, 4.0 rebounds and 3.2 assists per game during the regular season.
Denver's two-year commitment to Jeff Green, 34, comes on the heels of a string of one-year, veterans minimum contracts for him with the Cleveland Cavaliers, Washington Wizards, Houston Rockets, Utah Jazz and Brooklyn Nets.
As a key role player for the Nets last season, Jeff Green averaged 11 points and shot just over 41% from 3-point range.
He brings a plethora of playoff experience to Denver. He has played in 78 postseason games -- including last season in Brooklyn, when he put up 27 points in a Game 5 win over the Milwaukee Bucks in the Eastern Conference semifinals.
Jeff Green has averaged 12.8 points and 4.4 rebounds for his career. He played alongside Nuggets forward Aaron Gordon in Orlando during the 2016-17 season.
His deal includes $4.5 million in salary and $500,000 in unlikely performance bonuses.
Signed by Denver last offseason shortly after losing forward Jerami Grant to the Detroit Pistons, JaMychal Green provided value off the bench as a big who could space the floor and defend. He hit nearly 40% of his 3s while averaging 8.1 points and 4.8 rebounds in 19 minutes per game. JaMychal Green, 31, declined his $7.6 million player option for next season, which made him a free agent.
ESPN's Malika Andrews contributed to this report.