The Nobel-prize winner, who led Israel into peace talks with the Palestinians in the 1990s, had suffered a stroke two weeks ago.
President Obama led tributes saying: "A light has gone out, but the hope he gave us will burn forever".
US President Barack Obama has paid tribute to Shimon Peres as a man who "was rooted in his own unshakeable moral foundation and unflagging optimism".
Obama said Peres was "guided by a vision of the human dignity and progress that he knew people of goodwill could advance together".
Noting how he had fought for the nation's independence and served public office for seven decades, President Obama called Peres "the essence of Israel itself".
"A light has gone out, but the hope he gave us will burn forever".
President Obama has led tributes at the funeral of former Israeli prime minister and president Shimon Peres.
Former Israeli president Shimon Peres dies aged 93 following a stroke two weeks ago.