WASHINGTON — Michigan State University agreed to pay a record $4.5 million federal fine and the university’s provost resigned on Thursday after the Education Department determined that the school failed to report and address claims of sexual abuse by a former team doctor, Lawrence G. Nassar, who was convicted of sex crimes.

The fine was part of a settlement with the department, which initiated two investigations into the university’s handling of abuse by Mr. Nassar and the complicity of William Strampel, a former dean of the university’s College of Osteopathic Medicine. Mr. Nassar, a former doctor for the American women’s gymnastics team, was also an associate professor at the school.

The investigations revealed what department officials called “systemic failure to protect students from sexual abuse” over decades, and the university is now obligated to make sweeping changes to its campus safety operations.

“What transpired at Michigan State was abhorrent, inexcusable, and a total and complete failure to follow the law and protect students,” Education Secretary Betsy DeVos said in a statement. “Michigan State will now pay for its failures.”