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".
Chief Rabbi Ephraim Mirvis has paid tribute to Shimon Peres and described the former president and prime minister as a "true giant amongst men".
"There will be countless tributes to Shimon Peres over the coming days, but I fear that few, if any, will adequately capture the palpable sense of collective grief felt across the world, nor do justice to the memory of a true giant amongst men.
"It is true that Shimon Peres was a great statesman. He was the noblest of soldiers, a born leader, a uniquely talented diplomat, an inspiring speaker and a relentless campaigner.
"But, more significantly than any of those things, Shimon Peres was the greatest living example of an unshakable belief in the pursuit of peace against all odds."
He added: "No matter what the future holds, your legacy lives on in the Jewish people who will never rest until we achieve our eternal dream of peace among the peoples of the world."
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.