Virginia points guard Sean Singletary finished second with 14 votes.
Williams, who didn't start a single game this season and averaged 22 minutes per game, has posted 11.2 points and 6.4 rebounds while shooting 51 percent from the floor and 85 percent from the line. He's also 14-of-32 on three-point attempts.
"I'm just about winning games," Williams said earlier this season. "To me, it doesn't matter if I score 20 points a game or two points a game."
He is the sixth Tar Heel to earn the award and the first since Joseph Forte in 2000.