The defender led Brazil - hosts of this year's tournament - to victory at the 1958 World Cup in Sweden, which is also noted as being the breakthrough tournament for legendary striker Pele.
The South American side stormed to a 5-2 victory over Sweden in the final and Bellini is widely believed to have started the trend of lifting a trophy above the head in triumph.
"Brazilian football is mourning the death of a great man and captain," said Brazilian Football Confederation president Jose Maria Marin.
"I had the opportunity to meet him during his time at Sao Paulo where he proved, as well as being an excellent defender, he was a gentleman and an exemplary professional."
Bellini played for Vasco da Gama, Sao Paulo and Atletico Paranaense in his homeland, and won the World Cup again four years later.
He had suffered from Alzheimer's disease since 2011 and is reported to have died following complications from a heart attack.
He will be buried on Friday in Itapira, Sao Paulo.
