Anthony, 33, will form part of a new-look Thunder roster which has also been bolstered by the arrival of Paul George from the Indiana Pacers during the close season.
In return for Anthony, the Knicks will get center Enes Kanter, forward Doug McDermott and a second round 2018 draft pick.
The deal emerged on Saturday after Anthony agreed to waive his no-trade clause.
"We are thrilled to welcome Carmelo to Oklahoma City and the Thunder organization," Thunder general manager Sam Presti said in a statement.
"In addition to his skill level, experience, and unique talents, Carmelo is another high character, professional player for our roster."
Anthony, a 10-time All-Star and 14-year NBA veteran, heads to the Thunder after 976 career games in which he has averaged 24.8 points per game.
Knicks president Steve Mills thanked Anthony for his stint in New York.
"This is a deal we feel works for both this franchise and Carmelo," Knicks president Steve Mills said. "We thank him for his seven seasons in a Knicks uniform and all that he accomplished off the court for the City of New York by using his platform to address social issues."
Anthony meanwhile penned an open letter to Knicks fans on his website, thanking them for supporting him "through thick and thin."
Anthony is expected to be a key part of a revamped Thunder team which includes MVP Russell Westbrook as well as George.
Anthony said Monday a desire to play alongside Westbrook was behind his move.
"He was a big part, he was big reason why I wanted to come here," Anthony said of Westbrook.
"To see his loyalty to the city, to this organization, what he was able to do on the court, I wanted to be a part of that. Adding PG (Paul George) was just another reason why I wanted to come here."
Both Westbrook and George reportedly had a role in persuading Anthony to join the Western Conference side.
George told USA Today he had had formed a friendship with Anthony during spells on international duty with the US national team, and believed the trio could form a side capable of winning titles.
"This feels like a championship team," George said.
"I'm in a good place. I know Russ (Westbrook) is in a good place. Melo is motivated more than ever. You put us three together who all have something to prove still and we're going to be a special team."
source: news.abs-cbn.com
