Mr. Wolfe said he took responsibility for the anger and frustration on campus, asserting that conversations with community leaders, students, faculty, donors and others led him to his decision, more than just the football players’ threatened boycott.

“What was starting to become clear was the frustration and anger was evident, and it was something that needed to be done that was immediate and substantial for us to heal,” Mr. Wolfe said at a news conference.

As the two resignations were announced, the Board of Curators unveiled a slate of new initiatives to address racial tensions on campus, including hiring a diversity, inclusion and equity officer for the entire University of Missouri system. The university will also provide additional support to students, faculty and staff members who experience discrimination; create a task force to create plans for improving diversity and inclusion; and require diversity and inclusion training for all faculty, staff members and incoming students.

Josh Earnest, the White House press secretary, praised the protests as showing “that a few people speaking up and speaking out can have a profound impact.”

Officials said Mr. Loftin would remain at the university in a research role.

Opposition to the administration reached a peak in the last week. A graduate student, Jonathan Butler, who was a veteran of the Ferguson protests, held a highly publicized hunger strike, saying he would not eat again until Mr. Wolfe was gone. Protesters formed an encampment on campus. A coalition of Jewish groups told Mr. Loftin that they were “dismayed” by his lack of action after a swastika was drawn on a dormitory wall. Deans of nine of its schools called for Mr. Loftin’s removal.

On Monday morning, the student government demanded Mr. Wolfe’s ouster, and much of the faculty sent word to students that classes were canceled for two days, in favor of a teach-in focused on race relations.