Welsh delivered his resignation to university officials in the morning. In a statement, the school described Welsh's departure as being "in the best interests of the university and of the men's basketball program."
It was only 35 days ago when Hofstra excitedly announced Welsh's hiring, signing him to a $3 million, five-year contract that ranked as the largest in the school's history for a coach.
In an interview last night, Welsh would not say whether he received any financial incentive to resign.
Asked why he didn't fight to remain at Hofstra, he said, "Sometimes you have a feeling that things are best off the way they are . . . I just decided it was in the interests of Hofstra and my family to resign. We're going to move on."
University officials, including athletic director Jack Hayes, either did not return calls for comment or declined to speak Monday. Welsh's agent, Robert Ades, also did not return messages.
Welsh, 49, was arrested early Friday after police found him asleep at the wheel of his 2006 silver Lexus with his foot on the brake at a green light on Hempstead Turnpike. According to court records, he told police he had been returning from City Cellar, an upscale wine bar in Westbury, and his blood-alcohol level registered at .18 in a test taken two hours later, above the legal limit of .08.
Welsh pleaded not guilty to aggravated driving while intoxicated, driving while intoxicated and obstructing an intersection at his arraignment Friday. He is due back in First District Court in Hempstead for a hearing this morning.
"It is what it is, whatever happened, happened," Welsh said of the incident. "Life is full of challenges, ups and downs. Right now we'll bounce back, Hofstra will bounce back."
Hofstra responded swiftly Friday by suspending the coach immediately without pay.
Welsh had been living on campus ever since he was hired, but he moved into a hotel over the weekend. He had been planning to move his family into a rental June 1. He and his wife, who is pregnant, live in East Greenwich, R.I.
"What's next for me is caring for my family, my wife, my future son," he said. "I'll worry about what's next whenever I feel like thinking about it. Right now I'm just worried about my family."
Welsh's resignation leaves Hofstra without a basketball coach, and also in a quandary regarding the rest of the coaching staff. His assistant coaches have agreed to deals with Hofstra but they had not yet been announced, leaving them in limbo as the university opens up a search for a new head coach.
The attorney who is representing Welsh in his drunken driving case, Michael Dergarabedian of Rockville Centre, said he did not play a role in Welsh's meeting with school officials Monday or with Welsh's decision to resign.