Anthony informed the organization of his decision to sign on Tuesday after returning from Africa, where he attended the league's Africa Game and unveiled newly refurbished courts in the township of Soweto.
While terms of the deal have yet to be disclosed, it's believed that Anthony is coming aboard on a one-year contract for the veteran's minimum.
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Anthony was traded by the Oklahoma City Thunder to the Atlanta Hawks as part of a three-team deal on July 25 and was subsequently placed on waivers following a buyout, giving up just $2.4 million of his $27.9-million salary.
Houston had long been the favorites to ultimately land Anthony, who had reportedly been telling those around him that he expected to join the Rockets upon departing Oklahoma City.
One of the issues which hurt his tenure with the Thunder was his reluctance to accept a reserve role. In Houston, it's believed he'll be thrust into the starting lineup alongside cornerstones James Harden and Chris Paul at the three spot with former starter Trevor Ariza now with the Phoenix Suns.
Anthony's 2017-18 campaign was, by far, the weakest offensively of his 15-year career. The now 34-year-old averaged fewer than 20 points (16.2) for the first time, and posted career-low numbers in true shooting percentage (50.3) and player efficiency rating (12.7) while turning in his first negative value over replacement rating (-1.1).