Puskas, who suffered from Alzheimer's disease in the past six years, died in Kutvolgyi hospital in Budapest.
The former Real Madrid great was the inspirational of the superb Hungarian team during the 1950s, in a star-studded squad nicknamed the "Mighty Magyars".
He guided Hungary to the Olympic gold medal in 1952 and a second place in the 1954 World Cup in Switzerland.
Puskas scored a remarkable 83 goals in 84 appearances for Hungary before representing Spain at the 1962 World Cup in Chile.
On the club level, Puskas won with Real Madrid three European Cup titles and seven Spanish League trophies.
After announcing his retirement in 1967, Puskas turned to coaching and led Greek giants Panathinaikos to the European Cup final in the 1970/1971 season.
He had a spell with Egyptian side Masri in the late 1980s but did not succeed in helping the Port Said based club win titles.