He was capped 29 times by Wales and played four times for the Lions on the 1955 tour to South Africa.
After retiring at 28 he went on to have a distinguished career as a broadcaster.
Morgan's description of the sensational try scored by Gareth Edwards for the Barbarians against the All Blacks in 1973 is one of the most famous pieces of television commentary in sporting history.
"I have lost a friend and we have all lost one of rugby's greats who was also a true gentleman," WRU president Dennis Gethin said in a statement.
"His exploits as a player for Cardiff, Wales, the Barbarians and the British and Irish Lions are legendary but he also achieved so much off the field of play."