Hairston has not played this year due to eligibility questions concerning his possibly having received benefits that are not allowed by the NCAA.
After the school's lengthy investigation into the matter, Williams said Hairston's career at North Carolina had come to an end.
"I am extremely disappointed for P.J., his family and our team as he will no longer be playing basketball at North Carolina," Williams said. "P.J. made mistakes and I was very disappointed by his actions and now he is suffering the very difficult consequences. He is not a bad kid. He just made some mistakes."
The school has not released any information concerning the allegations that led to the decision, but the Raleigh News Observer had previously reported Hairston was arrested twice this year.
The newspaper said one of the arrests involved marijuana possession, although a charge against him was later dropped. The other was for speeding and reckless driving while he was behind the wheel of a vehicle he did not own.
Hairston has been suspended since July, when the school's investigation began.
"We first learned of this situation back in the summer and getting to this point took a great deal of time because the university, the NCAA and P.J.'s family took great care to learn as many of the facts as were possible to learn," North Carolina Athletic Director Bubba Cunningham said.
"I know everyone from P.J. and his family to the basketball team, our fans and the media, wanted this process to play out faster than it did. However, it took the time that was necessary and ultimately came to this difficult conclusion."
Hairston led North Carolina in scoring last season with an average of 14.6 points per game.
North Carolina guard Leslie McDonald played his first game of the season for the Tar Heels this week after missing nine contests due to his receiving impermissible benefits. He has been ordered to pay $1,783 to the charity of his choice.