Bonatti, who was also a journalist and a writer, died late on Tuesday and is to be buried in the northern Italian town of Lecco this weekend, reports say.
Reinhold Messner, another Italian mountaineering icon, hailed his friend Bonatti as “one of the greatest” and “a wonderful, tolerant and warm person”.
“The sports world and the whole of Italy mourn this extraordinary man, one of the most illustrious Italians in the history of mountaineering,” said Renato Schifani, the president of the Italian Senate, in a telegram sent to the Bonatti family.
Born in the northern city of Bergamo in 1930, Bonatti is widely viewed as one of the best-ever mountaineers, having climbed peaks in the Alps, Himalayas and Patagonia.
In 1965, he staged the first solo winter ascent of the north face of the Matterhorn, a decade after he carried out a solo climb of a new route on the south-west pillar of the Aiguille du Druin. Both are in the Alps.
He was at the centre of a controversy that lasted five decades after being accused by two fellow Italian mountaineers of having used oxygen bottles during a climb in 1953 of K2, the world’s second-highest mountain after Everest.
But in 2004, the Italian climbing club which the two mountaineers belonged to accepted Bonatti’s claim that he never used oxygen during the climb.