Carter, 35, will be beginning his 12th NBA season. He has spent the past four seasons with Denver, averaging 5.6 points and 4.5 assists in 204 regular-season games, the Nuggets said on their website (www.nba.com/nuggets).
He also has played for Miami, San Antonio and Minnesota.
Williams averaged 3.7 points and 2.7 points in 54 games with the Boston Celtics last season.
"We're excited to add two veteran players with playoff experience," Nuggets vice president of basketball operations Mark Warkentien said in a statement. "They are two more pieces to the puzzle as we work to improve our team this summer."
The Nuggets were 53-29 last season but lost in the first round of the playoffs to the Utah Jazz.
(Writing by Gene Cherry in Raleigh, North Carolina; Editing by Steve Ginsburg; To query or comment on this story email email@example.com)