Doctor Yerbi Fandau was the head of Starfleet Medical until 2379. In 2378, he contacted Beverly Crusher aboard the USS Enterprise-E and told her that he would be retiring the next year and offered her the position as his replacement.
As per standard protocol, Fandau also contacted Crusher's commanding officer, Captain Jean-Luc Picard, to inform him of the offer. It took Crusher almost a full year to decide, but eventually she did accept the position and took over for Fandau in late 2379. (TNG - A Time to... novels: A Time to Be Born, A Time for War, A Time for Peace)