Sir Edmund, who conquered the world's highest mountain in 1953, had been suffering health problems since April after suffering a fall whilst in Nepal.
His wife, Lady June Hillary said in a message to the nation that he was in good spirits until he died. "Sir Ed died peacefully this morning at 9am, his heart gave out," Stuff.co.nz quoted Lady Hillary, as saying in a message read by a family spokesman.
"He was 88. "He had been in good form and was looking forward to coming home and had remained in good spirits till the end. "The family are honoured to accept the Government's offer of a state funeral, recognising the impact he had on all New Zealanders," she said.
Mark Sainsbury, the family spokesman said that the family was comforted by messages of support from around the globe.
"His good friends the Sherpa people have called June and are organising their own memorial service in Nepal. The date for the funeral has yet to be set and will probably be done over the weekend as many relatives are overseas," he said.
Announcing Sir Ed's death, Prime Minister Helen Clark said his passing was a profound loss to New Zealand.
"My thoughts are with Lady Hillary, Sir Edmund's children, wider family, and close friends at this sad time," the PM said.