Mosbacher was born in White Plains, New York. He was the brother of Robert Mosbacher Sr., also a champion yachtsman, and U.S. Secretary of Commerce during the administration of President George Herbert Walker Bush. He was the son of Gertrude (née Schwartz) and Emil Mosbacher Sr., a wealthy stock trader who divested himself of his holdings just before the Wall Street Crash of 1929 and who, as a member of the Knickerbocker Yacht Club, helped formulate specifications for the Interclub class of racing sloops. His family was of German Jewish descent.