Anthony, 33, will waive his no-trade clause and his $8.1 million trade kicker to accommodate the deal, league sources told ESPN.
A trade call is scheduled for Monday to finalize the deal with the league office, sources said. Anthony is planning to arrive on Monday afternoon in Oklahoma City to take a physical and be available to practice Tuesday at the opening of the Thunder's training camp, according to league sources.
Anthony joins the league's reigning MVP, Russell Westbrook, and All-Star forward Paul George on a reshaped and formidable Western Conference contender. Westbrook and George -- who could become free agents in the summer of 2018 -- played a significant role in recruiting Anthony to waive his no-trade clause for Oklahoma City, league sources said.
The Thunder made a huge commitment with the Anthony deal, incurring $27.8 million in luxury tax for the 2017-18 season. The Thunder payroll will rise to $134 million this season. Anthony has two years, $54 million left on his contract, including a player option for $27.9 million in 2018-19.
Thunder general manager Sam Presti and Knicks GM Scott Perry had been talking on and off about a possible deal for weeks. Talks intensified in the 24 hours before Saturday's agreement, league sources said. As training camp loomed next week, Perry increasingly wanted no part of the circus that awaited his franchise with media day and Anthony's arrival both on Monday. Around the organization and Anthony, there was a belief that the unresolved saga would become a suffocating daily issue.
Perry started to feel the urgency of making a deal on Friday, and engaged Oklahoma City in more serious dialogue, league sources said.
The Thunder's assistant GM, Troy Weaver, who recruited Anthony to Syracuse, replaced Perry as the Thunder's assistant GM a decade ago. There are strong relationships between Presti, Weaver and Perry.
Once Anthony expanded his list of teams to include Cleveland and Oklahoma City within the past 10 days, Perry had more flexibility to move Anthony. Perry remained in contact with Portland Trail Blazers president of basketball operations Neil Olshey, who had the most versatile array of assets for New York and motivation to make the deal -- but, ultimately, Anthony would not accept a trade to the Pacific Northwest.
Anthony was intrigued with a potential partnership with Damian Lillard, CJ McCollum and Jusuf Nurkic, and the stability and track record of the front office and coaching staff in Portland, but did not want to make such a dramatic geographic shift, league sources said.
New York had been willing to do an Anthony deal with his preferred choice, Houston, that included Eric Gordon and Trevor Ariza, but the Rockets consistently rejected that idea, league sources said. Houston had become the focus of Anthony's trade request after the Rockets acquired All-Star guard Chris Paul, a close friend, in late June. But Houston needed a deal to include forward Ryan Anderson, who has three years and $60 million left on his contract.
Cleveland's package included Iman Shumpert and Channing Frye, and would've needed to be supplemented with minimum veterans, league sources said. Cleveland would never have considered including its 2018 first-round pick via Brooklyn, league sources said. New York had been pursuing a future first-round pick from Oklahoma City, but the Thunder were unable to acquire one as part of a larger deal for New York, according to league sources.
The 2018 second-round pick on its way to New York was part of Oklahoma City's deal with Chicago in February that brought McDermott and Taj Gibson to the Thunder. Gibson signed a free-agent contract with the Minnesota Timberwolves in July.
New York inquired about the Thunder's first-round pick at No. 21 in the 2017 draft, shooting guard Terrance Ferguson, but ultimately accepted the 2018 second-round pick that Chicago owed Oklahoma City. With the Bulls projected to be one of the worst teams in the league, that pick could be in early 30s of next June's draft.
The Thunder's odds to win the NBA title went from 20-1 to 16-1 at the Westgate after news of the trade. Their projected win total went from 51.5 to 52.5.
Westbrook has a five-year, $207 million extension offer on the table from the Thunder, with a deadline of Oct. 16 to sign. The Thunder will have a difficult time bringing back Westbrook, George and Anthony for the 2018-19 season; the repeater tax penalty would push the payroll ($157 million) and luxury tax ($143 million) skyward to make Oklahoma City the NBA's first $300 million payroll.
Kanter, 25, was a first-round pick of the Utah Jazz in 2011. He averaged 14.3 points and 6.7 rebounds for Oklahoma City last season, despite only playing 21.3 minutes per game.
Kanter posted a goodbye message to Oklahoma City fans on social media Saturday afternoon. He thanked the organization and the state of Oklahoma and added, "I want to say, please beat the Warriors for me. Please. I'm gonna be watching that game, so please beat the Warriors for me."
McDermott, 25, was the No. 11 overall draft pick in 2014. He was the NCAA's leading scorer that year, averaging 26.7 points per game as a senior at Creighton. He averaged 6.6 points and 19.5 minutes in 22 games for the Thunder after the February trade.
ESPN front-office insider Bobby Marks and NBA reporters Ramona Shelburne and Ian Begley contributed to this report.