Terms of the deal, announced by the National Basketball Association team on Sunday, were not disclosed.
Under NBA salary cap rules, Anthony could sign a five-year contract for as much as $129 million, but he may elect to take less in order to give the Knicks more budget room to try and improve the team by shopping for other free agents.
"After three months of questions around Carmelo Anthony's return to the New York Knicks, we are now happy to know that we have the cornerstone of what we envision as a 'team of excellence.'" Jackson said in a statement on the team website.
"(General manager) Steve Mills and I have assured Carmelo through our conversations, that we share the vision and the determination to build this team."
Anthony, who averaged 27.4 points last season for the Knicks was the biggest free agent on the market following Friday's decision by LeBron James to sign with the Cleveland Cavaliers.
"I am a New York Knick at heart," Anthony said. "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."
The Knicks have not won an NBA crown since 1973, when Jackson was a defensive-minded forward on the team.
Jackson has won a record 11 NBA titles as a coach including six with the Chicago Bulls and five with the Los Angeles Lakers and won a pair of titles as a player with the Knicks.
Anthony, 30, became a free agent by opting out of the final two years of a contract that would have paid him more than $23 million next season.
He had been hotly pursued by several teams including the Chicago Bulls, who were only able to offer him four years and $75 million due to their salary cap situation.
Knicks coach Derek Fisher, who won five championship rings while with Los Angeles under then-coach Jackson and will make his debut as a head coach this upcoming season, was thrilled to have Anthony on board.
"I have had the opportunity to be around some of the greatest players in our game, and now I have the honor of coaching Carmelo," Fisher said.
"This is an exciting time for the New York Knicks franchise and our fans. I look forward to working with him and building something special together."
Anthony, 6 feet 8 inches, 240-pounds, holds averages of 26.5 points, 7.1 rebounds and 3.1 assists in 226 games since coming to the Knicks in a three-team deal in February 2011.
This past season, Anthony posted the franchise's greatest single-game scoring performance - and a Madison Square Garden record - with 62 points versus Charlotte.
The re-signing of Anthony was top priority for Jackson, who last month made his first key personnel move by obtaining point guard Jose Calderon of Spain in a six-player trade that sent center Tyson Chandler to the Dallas Mavericks.
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