A source told ESPN The Magazine's Chris Broussard the two sides agreed to a four-year deal. Yahoo! Sports reported the deal was worth $44 million.
"Just signed with Denver, could not be happier! Thank you to the Kroenke family and the fans for their support," McGee tweeted Wednesday, along with a picture of him signing the contract.
McGee had two huge games against the Los Angeles Lakers in the playoffs, prompting coach George Karl to say: "I don't think I've ever coached a guy like this. He has the moves of a 6-6 player."
Earlier this summer, the Nuggets also re-signed free agent point guard Andre Miller.