Miura and his son Gota called them from the summit, prompting his daughter Emili to smile broadly and clap her hands in footage on public broadcaster NHK.
"I made it!" Miura said over the phone. "I never imagined I could make it to the top of Mt. Everest at age 80. This is the world's best feeling, although I'm totally exhausted. Even at 80, I can still do quite well."
The climbers planned to stick around the summit for about half an hour, take photos and then start to descend, his office said.
Nepalese mountaineering official Gyanendra Shrestha, at Everest base camp, confirmed that Miura had reached the summit, making him the oldest person to do so.
The previous oldest was Nepal's Min Bahadur Sherchan, who accomplished the feat at age 76 in 2008, just a day before Miura reached the top at age 75.
Sherchan, now 81, was preparing to scale the peak next week despite digestive problems he suffered several days ago. On Wednesday, Sherchan said by telephone from the base camp that he was in good health and "ready to take up the challenge."
Sherchan's team is also facing financial difficulties. It hasn't received the financial help that the Nepal government announced it would provide them. Purna Chandra Bhattarai, chief of Nepal's mountaineering department, said the aid proposal was still under consideration.
On his expedition's website, Miura explained his attempt to scale Everest at such an advanced age: "It is to challenge (my) own ultimate limit. It is to honor the great Mother Nature."
He said a successful climb would raise the bar for what is possible.
"And if the limit of age 80 is at the summit of Mt. Everest, the highest place on earth, one can never be happier," he said.
Miura conquered the mountain despite undergoing heart surgery in January for irregular heartbeat, or arrhythmia, his fourth heart operation since 2007, according to his daughter. He also fractured his pelvis and left thigh bone in a 2009 skiing accident.
Miura became famous when he was a young man as a daredevil speed skier.
He skied down Everest's South Col in 1970, using a parachute to brake his descent. The feat was captured in the Oscar-winning 1975 documentary, "The Man Who Skied Down Everest." He has also skied down Mt. Fuji.
It wasn't until Miura was 70, however, that he first climbed all the way to the summit of Everest. When he summited again at 75, he claimed to be the only man to accomplish the feat twice in his 70s. After that, he said he was determined to climb again at age 80.
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