ESPN reported the long-discussed formality would become official on Monday.
Anthony, 34, was amenable to a partial mid-level exception as his base salary after being one of the highest-paid players in the NBA last season and also receiving a buyout of his 2018-19 contract. Anthony receives the entire $27.9 million due from his previous deal.
Last season, unaccustomed to his role as power forward and playing alongside Russell Westbrook and Paul George, he averaged a career-low 16.2 points in 32.1 minutes in his lone season for the Thunder.
Anthony could be vital to the Rockets, who lost forwards Trevor Ariza (Suns) and Luc Mbah a Moute (Clippers) in free agency.
The Hawks acquired Anthony on July 25 as part of a three-team transaction, with Atlanta also receiving a protected 2022 first-round draft pick from the Thunder and Justin Anderson from the Philadelphia 76ers.
The Rockets created a roster opening by trading forward Chinanu Onuaku and cash to the Dallas Mavericks for center Maarty Leunen and the right to swap second-round draft picks in 2020. Onuaku played in six NBA games over the past two seasons and averaged 3.0 points and 2.3 rebounds.
Leunen, who turns 33 next month, has yet to appear in the NBA.
--Field Level Media