Sir Edmund Hillary was made an honorary Nepalese citizen
New Zealand Prime Minister Helen Clark described the explorer as a heroic figure and said all New Zealanders would deeply mourn his passing.
Sir Edmund's health had reportedly been in decline since April, when he suffered a fall while visiting Nepal.
He was the first man to climb the 8,850m (29,035ft) peak, with Tenzing Norgay, on 29 May 1953.
Returning to Everest's South Col camp, he famously greeted another member of the British expedition group with the words: "Well, George, we've knocked the bastard off."
After the ascent, Sir Edmund led a number of expeditions to the South Pole and devoted his life to helping the ethnic Sherpas of Nepal's Khumbu region.
His Himalayan Trust has helped build hospitals, clinics, bridges, airstrips and nearly 30 schools. He was made an honorary Nepalese citizen in 2003.
Prayer ceremonies are being held in Nepal to pay tribute to Sir Edmund, the charity says.
Announcing Sir Edmund's death in Auckland after a brief illness, New Zealand's prime minister described him as a "heroic figure who not only 'knocked off' Everest but lived a life of determination, humility and generosity".
"The legendary mountaineer, adventurer, and philanthropist is the best-known New Zealander ever to have lived," Ms Clark said in a statement.
"But most of all he was a quintessential Kiwi."
"He was ours - from his craggy appearance to laconic style to his directness and honesty. All New Zealanders will deeply mourn his passing."
Ms Clark said Sir Edmund's exploits would "continue to inspire new generations of New Zealanders, as they have for more than half a century already".
The BBC's Greg Ward in Auckland says Sir Edmund was arguably the most respected man in New Zealand.
His death has prompted an immediate outpouring of sympathy, with messages of condolences flooding in from around the globe, our correspondent says.
Tenzing Norgay's son called the death a great loss for humanity.
Race to the summit
The British adventurer and environmentalist, Pen Hadow, said Sir Edmund's death "closes one of the great chapters of planetary exploration".
"He was physically and metaphorically at the pinnacle of high adventure," the Dartmoor-based Arctic and Antarctic explorer told the Press Association.
Born in Auckland 19 July 1919, Sir Edmund began climbing mountains in his native country as a teenager and soon earned renown as an ice climber.
By the time he attempted his ascent of Everest in 1953 as part of an expedition led by the British climber, Sir John Hunt, seven previous expeditions to the top of the mountain had failed.
After a gruelling climb up the southern face, battling the effects of high altitude and bad weather, Sir Edmund and Tenzing Norgay managed to reach the peak at 1130 local time on 29 May.
"I continued hacking steps along the ridge and then up a few more to the right... to my great delight I realised we were on top of Mount Everest and that the whole world spread out below us," Sir Edmund said.
The two men hugged each other with relief and joy but only stayed on the summit for 15 minutes because they were low on oxygen.
Sir Edmund took several photographs of the scenery and of Tenzing waving flags of Britain, Nepal, the UN and India.
News of the conquest of Everest did not reach the outside world until 2 June, the eve of the Queen Elizabeth II's coronation.He was knighted by the Queen for his achievement in 1953, and 42 years later was awarded her highest award for chivalry - the Order of the Garter.