The Rockets have been working to move Anderson, 30, for more than a year. He has two years and $41 million left on his contract.
To clear the way for a trade out of Houston, Anderson agreed to reduce the guarantee on his $21 million salary in 2019-20 to $15.6 million, league sources told ESPN.
For the Suns, the $15.6 million represents Brandon Knight's salary for the 2019-20 season.
The Suns will have to decide by July 10, 2019, on guaranteeing the full amount for the final season of Anderson's contract, or they can waive him and owe him the $15.6 million. That financial concession will likely make trading Anderson an easier proposition for Phoenix, too.
For Anderson, there isn't a real financial risk adjusting his contract. Things can go well with Suns and they'll fully guarantee his $21 million. If not, he enters the 2019 free-agent market with $15.6 million in his pocket, significant cap space and chance to sign a new deal for multiple years.
Chriss was the No. 8 overall pick in the 2016 NBA draft but hasn't come close to fulfilling his potential. Knight has two years and $30 million left on his contract and missed last season because of a torn ACL.
The Suns traded for Anderson with an expectation that he could start at power forward. With the loss of Knight, the Suns plan to continue pursuing a trade for a starting-level point guard before the regular season.
Anderson's productivity dropped in each of his two seasons with the Rockets, averaging 9.3 points in 26.1 minutes per game last season. Anderson left New Orleans in 2016, signing a four-year, $80 million free-agent deal with Houston.
Melton, a shooting guard, was the 46th pick in the June draft out of USC.
Knight will get minutes in a reserve role behind Chris Paul.