Riva passed away at a hospital in Sardinia after reportedly suffering a heart attack over the weekend.
Nicknamed 'Roar of Thunder', Riva was widely regarded as one of the best players of his generation and notched up a remarkable scoring record during a 13-year playing career at Cagliari.
Born in Lombardy, Riva began his professional career in 1962 with local club Legnano before moving to Cagliari, where he scored 207 goals in 374 appearances across all competitions.
Riva is still Cagliari's all-time leading scorer and sits over 100 goals clear of the nearest challenger Luigi Piras (104) in second place.
The striker scored 21 goals to help Cagliari win their first and only Serie A title to date in 1970, and in 2005 the Islanders retired the No.11 shirt to honour his legacy.
Riva, the runner-up for the 1969 Ballon d'Or, also excelled at international level and scored a record 35 goals in 42 appearances for the Azzurri between 1965 and 1974.
He helped Italy win the 1968 European Championships before they reached the World Cup final two years later, losing 4-1 to a Pele-inspired Brazil side.
After hanging up his boots, Riva managed the Italy national team for 25 years and successfully led the Azzurri to their fourth World Cup in 2006, beating France on penalties in the final held in Berlin.
A statement from Gabriele Gravina, the president of the Italian Football Federation (FIGC), read: "I'm shaken and profoundly saddened, Italian soccer is grieving because a real and proper national hero has left us.
"Gigi Riva was the embodiment of a great man and an extraordinary footballer: his pride, his class and his sense of fairness united generations.
"Thanks to him we won the European Championship in 1968 and the World Cup in 2006 [as team manager]."
Fellow Italian icon Dino Zoff said: "I'm losing a great friend, we've had a long life together. From the military to many memories in the national team. Infinite sadness, I'm deeply saddened, I can't speak."
The FIGC have plans in place to ensure that a minutes silence will be held before all matches across Italy in honour of Riva for the rest of this week.