Morgans was taken ill on Saturday and later passed away in hospital, the Manchester United website reported.
The Welshman made his debut for United against Leicester City on 21 December 1957 at the age of 18.
He was injured when the plane carrying United home from a European Cup tie in Belgrade crashed on February 6, 1958 after a refuelling stop at Munich, killing 23 of the 44 people on board.
Morgans was found later that evening in the wreckage by two German reporters. He was able to continue his playing career and left Old Trafford in 1961 to join Swansea City and later Newport County before retiring in 1967.