The team gave the free agent McGee a four-year contract worth $44 million, according to local reports.
McGee, who was acquired by the Nuggets in a March trade with the Washington Wizards, showed flashes of big-time potential and averaged 11.3 points, 7.8 rebounds and 2.16 blocks per game.
The 24-year-old was particularly strong during the playoffs, where the Nuggets pushed the Los Angeles Lakers to a tough seven-game first-round series.
"JaVale did a tremendous job for us after the trade," Nuggets executive vice president of basketball operations Masai Ujiri told the team's website.
"He worked hard on the court and did everything our coaches asked of him. Plus, he's only 24 years old. With our coaching staff, he's only going to get better."