"Carmelo has been an important part of the best seven-year stretch in Denver Nuggets history," said Nuggets president Josh Kroenke on the team's website.
"We have shared many special moments and were fortunate to watch him grow into an All-Star and one of the league's top players.
"However, Carmelo made it very clear early in the season that he wasn't willing to re-commit to the organisation and wanted to pursue other opportunities in basketball and life.
"At that point, we decided it was imperative that we do what was in the best interest of the Denver Nuggets and our fans."
There had been speculation about the sharp-shooting Anthony's future throughout the season with the Knicks at the centre of trade talk.
The 26-year-old Brooklyn-born Anthony will team up with fellow All-Star Amare Stoudemire in what is the latest concentration of power in the NBA.
Anthony is expected to make his New York debut on Wednesday when the Knicks host the Milwaukee Bucks.
Along with Anthony, guards Chauncey Billups and Anthony Carter, center Shelden Williams and forward Renaldo Balkman will go to New York.
Heading in the opposite direction are guard Raymond Felton, forwards Danilo Gallinari and Wilson Chandler and Russian center Timofey Mozgov.
On top of those players, Denver will also get the Knicks' first-round pick in 2014 and second-round picks in 2012 and 2013 plus $3 million in cash.
"We are excited about the talented young players we acquired in this trade," Kroenke said. "They were valuable contributors to one of the most improved teams in the NBA this season.
"We are looking forward to making another postseason push.
"Our goals remain the same: improve every day, play hard every game and bring an NBA championship to Denver."