Williams allegedly attacked Buscemi on May 8 on Third Avenue near East 27th Street in Kips Bay, Manhattan, according to police.

NYPD said it was searching for a “male with dark complexion” wearing a dark baseball cap, a blue T-shirt, black pant and white sneakers, and carrying a book bag.

Police since then had been scouring the city for Williams, including at a Brooklyn homeless shelter believed to be his last known address.

Superintendents at the shelter on Friday called police because Williams had been acting aggressive over personal items he believed were stolen.

Police said an officer responding to the incident asked Williams to fill out a report for his lost property. The officer recognized his name and linked it to a photo of the person wanted in Buscemi’s assault.

The officer showed Williams an NYPD wanted poster and asked, “Is this you?” Williams allegedly confessed that it was.

Buscemi’s publicist gave the news of the assault earlier this week.

“Steve Buscemi was assaulted in Mid-Town Manhattan, another victim of a random act of violence in the city,” a statement from his publicist read. “He is ok and appreciates everyone’s well wishes.”

Buscemi was treated at Bellevue Hospital for bruising, swelling and bleeding to his left eye.

He was seen sporting a black eye on May 11 at a commercial shoot in Soho.

Buscemi is a Brooklyn native and former firefighter who helped his former FDNY unit in the fallout of the 9/11 terrorist attacks.

His acting career includes roles in “Fargo,” “The Big Lebowski,” “Reservoir Dogs” and the starring role in HBO’s “Boardwalk Empire.”

He’s the second “Boardwalk Empire” cast member to get jumped on the streets of New York City. Co-star Michael Stuhlbarg was randomly attacked by a man with a rock in March while walking in Central Park.

Stuhlbarg chased down his attacker and held him until police arrived and took him into custody.