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".
Gordon Brown has said Shimon Peres will be mourned around the world.
The former prime minister said: "Shimon Peres will be remembered as a peacemaker - mourned on every continent by men and women committed to ending war.
"He understood the importance of negotiation because he understood the cost of war. He was not an idealist for peace out of vision alone but because he had lived through times of conflict.
"His personal journey through life challenges us all to think how best we can promote peace and reconciliation."
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.