His daughter Emiri, 52, said: "I believe he will keep on going even when he turns 90 or 100."
Miura was on his way back down the mountain Thursday, a Nepalese tourism official said, confirming the successful ascent.
"He reached the summit this morning and is currently descending to Camp Four," the official, Gyanendra Shrestha, told AFP from Everest Base Camp.
Banner headlines in Japanese evening papers proclaimed the elderly adventurer's success and television news carried extensive coverage of the feat, which was widely celebrated in a nation increasingly dominated by older people.
It was Miura's third conquest of the 8,848-metre (29,028-foot) peak.
He previously reached the summit in 2003 and 2008 when he was 70, claiming the oldest summiteer record, and 75 respectively.
His 2003 record was broken in 2007 when fellow Japanese Katsusuke Yanagisawa reached the top at the age of 71.
His second conquest of Everest was made in May 2008 but he was beaten to the summit by Sherchan, who had got there just one day earlier at the age of 76.