Eichorst will replace Tom Osborne, Nebraska's former football coach who announced last month he will retire as the school's athletic director at the end of the year. Eichorst has been the athletic director at Miami for 18 months.
"It is truly an honor and privilege to be a part of one of the great universities in America and one of the strongest athletic departments in all of college sports," Eichorst said.
Eichorst's tenure at Miami included a scandal involving football players who the NCAA said received impermissible benefits from a Florida businessman who is now serving a prison term for running a Ponzi scheme.
Eight players were suspended.
Donna Shalala, president of the University of Miami, said Blake James had been appointed that school's AD. He has served as senior associate athletic director.