He suffered a stroke two weeks ago and his condition 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.
Mr Peres, who was one of the last of a generation of Israeli politicians present at the new nation's birth in 1948, served twice as the country's prime minister and once as president.
He won the Nobel Peace prize in 1994 for his role negotiating peace accords with the Palestinians a year earlier.
He once said the Palestinians were Israel's "closest neighbours" and might become its "closest friends".