League sources also told Broussard that none of the teams can officially confirm the deal until Tuesday.
The swap is a three-way deal including Minnesota, a league source told Broussard.
As a part of the deal, the Knicks will send Wilson Chandler, Raymond Felton, Danilo Gallinari,Timofey Mozgov, and a 2014 first-round draft pick to the Nuggets, who would get additional picks and cash, league sources told Broussard. Along with Anthony, New York would acquire Chauncey Billups, Shelden Williams,Anthony Carter and Renaldo Balkman, the sources said.
New York will send Anthony Randolph and Eddy Curry to Minnesota as part of the deal in exchange for Corey Brewer, a league source told Broussard.
The Denver Post first reported the news.
"I'm glad its over," Nuggets coach George Karl said, according to the newspaper. "I'm glad it's an opportunity to reinvent. I think everybody handled it as classy as you could handle it. There's some sadness to it, there always will be."
The Nuggets have explored an Anthony trade since he refused to sign the three-year contract extension worth nearly $65 million they offered him last summer. They appeared on the verge of sending him to the New Jersey Nets on multiple occasions, but the Knicks increased their offer enough to land Anthony, who was believed to prefer New York all along.
The Knicks would hope he could be in uniform Wednesday when they host the Milwaukee Bucks.
Anthony wasn't at the Nuggets' practice on Monday night. Instead, the All-Star forward was in Burbank, Calif., taping a segment on "Conan."
Anthony, who has been the subject of intense speculation as Thursday's trade deadline approaches, stayed behind in Los Angeles following the NBA All-Star Game while his teammates gathered at the Pepsi Center.
Team spokesman Tim Gelt told The Associated Press that Anthony's absence was excused. Late Monday afternoon, Anthony tweeted: "Headed to Burbank to film THE CONAN SHOW."
Anthony led the Nuggets to the playoffs in each of his first seven seasons in Denver after winning a national title at Syracuse as a freshman and had them positioned for another playoff run this year. But Denver advanced out of the first round just once in that time.
He stood to become the headliner of the 2011 free agent class, but didn't want to risk free agency knowing a new collective bargaining agreement could cost him millions. But once he refused the extension with the Nuggets -- plus put his Denver mansion on the market last year -- the Nuggets' new front office team of general manager Masai Ujiri and team president Josh Kroenke had to begin trade talks so they wouldn't risk losing him for nothing like the Cavaliers did with LeBron James and the Toronto Raptors did with Chris Bosh last year.
There were persistent rumors Anthony wouldn't take the extension if traded to the Nets, which was a prerequisite for them agreeing to a trade. He instead gets his apparent wish to join a Knicks team that is in sixth place in the Eastern Conference and in position for its first playoff berth since 2004.