The 30-year-old Williams, a veteran of 11 NBA seasons, averaged 11.7 points, 6.4 rebounds and 1.4 assists in 28.9 minutes per game while starting all 81 contests in which he appeared.
The 6-foot-9 forward earned $7 million last season in the final year of a two-year, $14 million contract with the Hornets. The No. 2 pick of the Hawks in the 2005 draft, Williams spent seven seasons with Atlanta before his two years with the Utah Jazz.
After the 2015-16 season, Williams, who played collegiately at North Carolina, stressed the benefit of the Hornets keeping their core together.
"I feel like any time, especially in pro sports, when you keep a group of guys together for three or four years, whatever the case may be, you can do some really good things," Williams told reporters.
Information from ESPN's Chris Forsberg was used in this report.