The versatile and popular player, who could play at centre half or centre forward, was part of the Wales 1958 World Cup squad.
He began his 20-year career in his hometown Swansea - netting six goals in 233 league appearances.
Officials at the Welsh side said that Charles - who was the younger brother of Juventus and Leeds great John Charles - died peacefully on Saturday.
Club coach Alan Curtis said Charles was a much loved part of the club and the local community.
He said: “It’s a sad, sad loss.
“Mel was part of a huge sporting family in Swansea.
“Not only was he highly respected as a footballer, he was a fantastic character who enjoyed life to the full. Everybody loved to be in his company.
“There is no doubt he will go down as one of Swansea and Wales’ greatest players and will now join that great football team in heaven.”
Charles grew up in the Cwmbwrla area of Swansea along elder brother John and three sibilings.
At the age of 17, he signed a professional contract with his hometown team and made his debut in 1952.
After his role in the Wales’ 1958 World Cup team, Charles soon found himself in demand from several big clubs.
In 1959, he opted to join Arsenal in a fee worth £42,750, a then British transfer record.
However, his time at Highbury was hampered by injuries and in 1962 he returned to Wales - signing for the Swans’ arch-rivals Cardiff City before spells with Porthmadog, Port Vale and Haverfordwest.
Four years after retiring in 1972, history would end up repeating itself when his son Jeremy signed for Swansea.
Former club and international teammate Mel Nurse described Charles as a big character who was loved both on and off the field.
He said: “We were brought up together with his brother John.
“We went to Cwmbwrla and Manselton schools. I followed him on and off the field. I will miss him.
“He was a big character - Swansea has lost a legend.
“Anyone who had anything to do with Mel knew he was a big personality. He will be sorely missed.”
A Swansea City spokesman added: “We are sorry to hear of the loss of a club great and true gentleman.
“Our thoughts and prayers are with his family and friends at this sad time.”