Morrison, who controlled the 1995 World Cup final between South Africa and New Zealand as the highlight of an illustrious career, will succeed Colin High.
High, 66, is to retire next June after six years in the post.
Morrison's current position as RFU elite referee development officer will be filled by another former Test match official Tony Spreadbury, who will work alongside fellow development officer Brian Campsall.
RFU elite rugby director Rob Andrew said: "Colin has been an outstanding member of the elite rugby and referee unit.
"His enthusiasm and knowledge of the game has been instrumental in English referees being widely regarded as some of the best in the world."