The deal will be worth $5 million, Charania added.
Williams joined the Hawks late in the season following a straight-up trade with the Clippers for Rajon Rondo.
Williams, 34, is 6-foot-1 and has spent most of his career as the ideal reserve, winning Sixth Man of the Year honors on three occassions.
He appeared in 66 games overall last season, averaging 11.3 points, 3.4 assists and 2.1 rebounds. He averaged 10.0 points in 24 regular-season games with the Hawks, followed by 7.7 points in the playoffs, whe Atlanta made an inspirational run to the Easter Conference finals.