Drake’s appointment was announced at a meeting of the Ohio State Board of Trustees, where he was described as the “strongest and consensus candidate.”
Drake, 63, will become the Ohio institution’s first African American president and will replace E. Gordon Gee, who retired in July.
At the Irvine campus, Drake led efforts to increase representation of minority and low-income students and diversify faculty ranks.
He helped to enhance the campus' reputation as a top center of research as well as repaired the reputation of the school's medical center, which faced scrutiny over its liver transplant program.
He was criticized, though, over handling of a protest by Muslim students during a speech by the Israeli ambassador and the naming of a new dean at the law school.
Drake graduated from Stanford University and received an MD from UC San Francisco, where he spent more than two decades on the faculty as a professor of ophthalmology.
Previous to the Irvine post, he was vice president for health affairs for the University of California system.