As two-time prime minister, minister of defence, foreign affairs, finance and transportation; and, until 2014, as president, Peres did more than anyone to build up Israel's formidable military might and the country's nuclear programme.
Israeli Prime Minister Benjamin Netanyahu hailed Peres as a "great man of the world".
"He soared to incredible heights. He was a great man of Israel; he was a great man of the world. Israel grieves for him, the world grieves for him, but we find hope in his legacy, as does the world," Netanyahu told mourners at Mount Herzl national cemetery where Peres would be buried alongside other prominent leaders of the Jewish state.
Obama, who awarded Peres the presidential Medal of Freedom in 2012, is one of the speakers at the ceremony. He arrived in Israel this morning. He wore a black Jewish skullcap as he took his seat at the ceremony.
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Palestinian Authority President Mahmoud Abbas was also among attendees. He was seated in the front row.
Abbas, who is on his first visit to Israel since September 2010 when peace talks broke down, shook hands and spoke briefly with Netanyahu upon arrival.
Egyptian Foreign Minister Sameh Shoukry and Jordanian Prime Minister Jawad Anani were also in attendance.
Jordan's King Abdullah II yesterday sent a condolence letter to Israeli President Reuven Rivlin in which he highlighted Peres' efforts to bring peace between Israel and the Palestinians as part of a two-state solution.
Egypt and Jordan are the only two Arab countries to have signed peace treaties with Israel.
Israel's President Reuven Rivlin in his eulogy at the funeral ceremony credited Peres with ensuring the State of Israel "as an indisputable fact".
Applauding Peres as the visionary who shaped Israel's
future right from its foundation, the Israeli President said that he was not just a thinker but a doer.
"You had the rare ability Shimon to conceive what seemed to be the inconceivable, and see it to fruition. Your eyes saw far ahead, while your feet covered great distances on the landscape of Jewish and Zionist history," Rivlin said.
Peres, who was the pioneer of Israel's nuclear programme and also backed the creation of Jewish settlements in the earlier years only to abandon the idea later as a peacemaker, earned praise for his contributions to Israel's security.
"How deep was your belief in the sacred combination of ethical leadership and military prowess, that Israel must act not just with wisdom, but with justice, faithful at every moment to its values as a Jewish and democratic state, democratic and Jewish," the president added.
Former US president Bill Clinton was among those who paid their last respects there.
Security forces were put on high alert as the funeral began, with roads closed and thousands of officers deployed.
Some 2000 police officers backed by personnel from other agencies have been deployed in Jerusalem for the ceremony with media reports saying that some Arab and Jewish suspects have been put under preventive arrest to prevent any disruption.
Earlier, the casket carrying the departed soul was moved from the Knesset plaza to Mount Herzl.