The Vertical's Shams Charania reported Monday morning Williams agreed to a three-year contract worth $17 million.
Williams spent his first two NBA seasons with the Suns after going undrafted out of UC Santa Barbara. He was a solid contributor off the bench last season, averaging 17.6 points and 14.8 rebounds per 36 minutes in 47 games, per Basketball-Reference.com.
Mika Honkasalo of HoopsHype.com wrote: "As an undersized center, Williams has limitations on both ends of the floor but does his best to make up for his weaknesses with a motor that doesn't stop."
The Suns will be banking on that relentless attacking style.
Although Phoenix looks to have little chance of competing in the stacked Western Conference in 2017-18, Williams adds to a promising young core.
Williams (24) joins Devin Booker (20), Marquese Chriss (20), Josh Jackson (20), Tyler Ulis (21) and Dragan Bender (19) in this youth-infused roster.