Mr. Peres suffered a stroke two weeks ago. His condition had improved before a sudden deterioration on Tuesday.
His son Chemi led tributes to “one of the founding fathers of the state of Israel” who “worked tirelessly” for it.
World figures are expected to attend his funeral in Jerusalem on Friday, including US President Barack Obama, Prince Charles and Pope Francis.
Mr. Peres was one of the last of a generation of Israeli politicians present at the new nation’s birth in 1948.
He won the Nobel Peace Prize in 1994 for his role negotiating the Oslo peace accords with the Palestinians a year earlier, a prize he shared with Prime Minister Yitzhak Rabin, who was later assassinated, and Palestinian leader Yasser Arafat.
He once said the Palestinians were Israel’s “closest neighbours” and might become its “closest friends”.
Mr. Peres died in a hospital near Tel Aviv early on Wednesday, with his family at his bedside. He “left us without suffering”, said Rafi Walden, his son-in-law and personal physician.
He had been in the intensive care unit of the Sheba Medical Centre after suffering a major stroke on 13 September.
The funeral will be held on Friday at Mount Herzl in Jerusalem, Israel’s national cemetery.
Mr. Peres’s son, Chemi, said of his father: “He served our people before we even had a country of our own. He worked tirelessly for Israel from the very first day of the state to the last day of his life.”
“My father used to say – and I’m quoting – ‘You are only as great as the cause you serve,'” he added.
Israel’s Prime Minister Benjamin Netanyahu expressed his “deep sorrow” over Mr. Peres’ death.
“As a man of vision, his gaze was aimed to the future,” he said in a video statement.