The former Ferencvaros forward, who turned 70 last month, won Europe's top individual award in 1967 and made 75 appearances for his country, scoring 31 goals.
He died following complications after heart surgery last week, the FA reported.
Born in the village of Hercegszanto in southern Hungary in September 1941, he became known as "The Emperor" in his homeland, and stayed a one-club player for his whole career.
Despite the brilliance of the Hungary's Magical Magyars team of the early 1950s, the European award, which began in 1956, passed them by and Albert remains the only Hungarian to win the honour.
"You know what is so special about the Golden Ball - the defenders never took it away from me," he told Nemzeti Sport, Hungary's daily sports newspaper on his 70th birthday last month.
Albert's son, Florian Albert Jr, also played for Ferencvaros and Hungary and the club's stadium is named after him.
