The deal includes $74 million in guaranteed money, and team and individual bonus clauses worth the remaining $10 million, league sources said.
Harris' agents with CAA Sports, Austin Brown and Aaron Mintz, completed the deal on Saturday night with Denver president of basketball operations Tim Connelly.
Harris, 23, is eligible for his rookie extension as part of the NBA's 2014 draft class. There's an Oct. 16 deadline for players to agree to a deal, or proceed into restricted free agency in July.
Harris and center Nikola Jokic have developed into the cornerstone talents of the Nuggets' talented young core.
Harris' extension, which begins with the 2018-19 season, represents a dramatic rise for a 19th overall draft pick who overcame a poor rookie season in the NBA.
Last season, Harris averaged 14.9 points on 50 percent field goal shooting and 42 percent on 3-pointers.
Harris' progression this preseason, including a 25-point, 21-minute performance against the Los Angeles Lakers, has further solidified his standing as one of the NBA's elite young shooting guards.
He will rank in the top 10 in salary for shooting guards in 2018-19, joining James Harden, DeMar DeRozan, CJ McCollum, Bradley Beal, Nicolas Batum, Victor Oladipo, Jimmy Butler, Klay Thompson and Wesley Matthews in the top 10.
Harris' deal eliminates one more possible restricted free agent from the market in the summer of 2018. With limited salary-cap space on the market, restricted free agency promises to be an uncertain proposition for players. Next summer's market of unrestricted free-agent shooting guards could include Philadelphia's JJ Redick, Detroit's Avery Bradley, the Lakers' Kentavious Caldwell-Pope, San Antonio's Danny Green and Indiana's Glenn Robinson III.
Information from ESPN's Bobby Marks was used in this report.