The 30-year-old had opted out of his contract at the end of the season to test the free-agent market, but has decided to return to the Knicks after agreeing a reported five-year deal worth $120m (£70m).
Anthony said on his official website: "This organisation has supported me and in return, I want to stay and build here with this city and my team. At this pivotal juncture in my career, I owed it to myself and my family to explore all of the options available to me. Through it all, my heart never wavered.
"During this journey I met with some quality organisations who have amazing talent and leadership. I thank them for their consideration, belief in my talent, and opportunity to imagine the possibilities.
"I will always remember this chapter in my life. In the end, I am a New York Knick at heart. I am looking forward to continue my career in orange & blue and to work with Phil Jackson, a champion who builds championship teams. Madison Square Garden is the mecca of basketball and I am surrounded by the greatest fans in the world."
Anthony averaged 27.4 points per game for the Knicks last season.