The Welshman, who survived the Munich air disaster in 1958, was taken ill on Saturday evening and later passed away in hospital.
Morgans made his debut for United in December 1957 in a fixture against Leicester City.
"Staff at the football club send their deepest condolences to Kenny's family and friends," read a statement on the club's official website.
Having recovered from his injuries sustained in Munich, Morgans moved on to Swansea City in 1961. He then joined Newport County before retiring from football in 1967.