He and his wife met as undergraduates at the University of Exeter in England. She became a teacher, and worked most recently with adult students learning English as a second language. Dr. Hamilton got his master’s degree from the University of British Columbia and his Ph.D. from the University of Cambridge. He did postdoctoral work at the Université Louis Pasteur, in France, moving to the United States in 1981 to take a job teaching at Princeton. He was a professor and then chairman of the chemistry department at the University of Pittsburgh, and spent 14 years at Yale as a professor and administrator.

While he was at Oxford, the university opened a new school of government, expanded its business school, modernized its medical school and hospital and renovated some of its oldest libraries and museums. As vice-chancellor, Dr. Hamilton proved to be an adept fund-raiser who had no qualms about asking rich people for money. He helped start a 3-billion-pound capital campaign (about $4.22 billion), of which £2 billion has been raised so far. The skill will come in handy at N.Y.U., whose endowment, $3.5 billion, is paltry when compared with Harvard’s ($37.6 billion) and Yale’s ($25.6 billion).

“Andy has a kind of zest and positivity and ebullience about the way in which he approaches fund-raising that makes everybody feel good,” said Sally Mapstone, Oxford’s pro-vice-chancellor for education. “Though Andy is quintessentially British in the way he sounds, he has a certain amount of chutzpah when it comes to being with and talking to people in a philanthropic setting.”

As provost at Yale, Dr. Hamilton helped revitalize the undergraduate curriculum, recruited minority and female faculty members and was instrumental in promoting Yale’s $109 million purchase of a vast property seven miles outside of New Haven, now known as the west campus, and in turning it into a multidisciplinary science and medical hub.

“He had a broad vision to take a project and say, ‘What do we want to accomplish, what faculty do we need to hire to accomplish that and what facilities do we need to build?’” Peter Salovey, president of Yale, said in an interview. “And then he knows how to engage a process that allows many voices and many stakeholders to be heard.”

On a January morning soon after the first storm of 2016 left more than two feet of snow on New York City, Dr. Hamilton was sitting in his large office, looking out the window toward Washington Square Park and beyond. The office — plainly constructed, in a kind of utilitarian, light-wood ski-chalet sort of way — was virtually devoid of embellishments or accouterments. None of Dr. Hamilton’s things had yet arrived from England.