Yale University’s new president will be Maurie D. McInnis, currently the president of Stony Brook University, a New York state public university where she is known for raising the school’s profile, donations and prestige.

When she takes over from Yale’s outgoing president, Peter Salovey, in July, Dr. McInnis, who earned masters and doctoral degrees from Yale in the 1990s, will become the university’s first permanent female president.

Her selection followed a search that began last fall. The delay in announcing a successor for Dr. Salovey, who leaves his post at the end of June, prompted speculation that the university’s selection committee was having difficulty finding someone during a tumultuous time on university campuses.

Joshua Bekenstein, a founder of Bain Capital who heads the Yale Corporation, the university’s governing board, said the search committee had undertaken a “very thorough” selection process.

“We felt it was important to do all the work,” he said. Expressing confidence in Dr. McInnis, he added, “She’s going to do a wonderful job.”

Dr. McInnis, who serves on the Yale board, will assume the presidency at a tumultuous time, when universities face challenges stemming from last year’s Supreme Court decision banning race-conscious admission and from the likely continuation of pro-Palestinian protests over the Israel-Hamas war.

As if to underscore the dangers she may face, a group of 200 professors calling themselves Scholars for the Public Good began within minutes after the announcement to circulate a letter urging Dr. McInnis to resist pressures from donors and politicians who are seeking to undermine campus diversity, free expression and educational excellence.

In a brief interview on Wednesday, Dr. McInnis said she was committed to maintaining a diverse campus at Yale, in New Haven, Conn., despite the Supreme Court’s ruling last year.

“My deep commitment to advancing opportunities for students and for our prospective students is steadfast, certainly in my work at Stony Brook, and that will continue at Yale,” Dr. McInnis said in the interview, adding, “And none of that changes with the court ruling.”

Yale has not yet released demographic information about its incoming class.

Dr. McInnis survived a censure vote by the faculty senate at Stony Brook following her decision to arrest campus protesters there in May. Defending that decision on Wednesday, she said: “No president wants to have to request that authorities intervene to disperse student protesters. And once we realized they would not disperse, everything proceeded in a calm and orderly manner.”

At Stony Brook, Dr. McInnis, 58, secured a $500 million donation from the Simons Foundation and won a competition to lead the creation of a state climate-change campus on Governors Island in New York City.

Lisa Benz Scott, a professor who heads Stony Brook’s public health program, applauded Dr. McInnis’s leadership during the pandemic, and said Dr. McInnis was “hands on” with students.

“You could see her in a pair of jeans and a Stony Brook T-shirt at student events,” Dr. Benz Scott said.

Richard K. Larson, the head of Stony Brook’s faculty senate, agreed that Dr. McInnis performed “brilliantly” during her first three years as Stony Brook’s president, but he faulted her more recent stewardship.

“Where things got much more difficult, and where this administration reached its sell-by date, was in the last year,” Dr. Larson said, criticizing Dr. McInnis’s decision to have protesting students arrested. That was why the vote on the censure motion was so close, failing by 51 votes to 54 with three abstentions, according to Dr. Larson, a professor of linguistics.

Before joining Stony Brook, Dr. McInnis had served as provost at the University of Texas, where she was sometimes seen rowing single scull crew on Lady Bird Lake. She spent much of her earlier career at the University of Virginia, where she received her undergraduate degree and later served both as a professor and as vice-provost.

Dr. McInnis’s academic field is art history. Much of her scholarship has focused on the interplay of arts and politics, particularly the politics of slavery. Her most recent book, published in 2019, is “Educated in Tyranny: Slavery at Thomas Jefferson’s University.”

Though Dr. McInnis is set to become the first woman to serve as the permanent president of Yale, the university has been headed by a woman once before, when the historian Hanna Holborn Gray was chosen in 1977 as interim president. Dr. Gray went on to serve as president of the University of Chicago, and is currently a professor emerita there.

Reflecting on her own history-making selection, Dr. McInnis said she was well aware of how she could serve “as a role model for other women aspiring to leadership positions.”