The 93 year-old Mr Peres was a popular figure in Israel, serving twice as prime minister, then as president from 2007 until 2014.
In 1994, he was awarded the Nobel Peace Prize.
Just hours before the stroke that put him in hospital, Shimon Peres posted a Facebook video urging Israelis to buy locally made products.
"I recommend all of us, all of you, to buy 'blue and white' Israeli products, not only because it is more patriotic, simply because it's better."
Born in Poland in 1923, Shimon Peres emigrated to what was then the British-ruled mandate of Palestine when he was 11 years old.
He joined the Zionist fight in the 1940s and entered parliament in 1959.
He became Labor prime minister in 1984 and served in the same post again in 1995.
As foreign minister in 1993, Mr Peres played a key role in the Oslo Accords between the Israelis and Palestinians that brought hope for a wider peace in the Middle East.
The agreement was signed at the White House, where then United States president Bill Clinton hailed the achievement.
"A moment when we dare to pledge what, for so long, seemed difficult even to imagine, that the security of the Israeli people will be reconciled with the hopes of the Palestinian people and there will be more security and more hope for all."
The next year, Mr Peres, then Israeli prime minister Yitzhak Rabin and then Palestine Liberation Organisation chairman Yasser Arafat were awarded the Nobel Peace Prize.
Shimon Peres expressed high hopes.
"Israel's role in the Middle East should be to contribute to a great, sustained regional revival, a Middle East without wars, without enemies, without ballistic missiles, without nuclear warheads."
An Israeli law student unhappy with the agreement assassinated Yitzhak Rabin in 1995, leading to Shimon Peres's second term as prime minister.
He stepped in as acting prime minister, but then lost power at the 1996 elections to the current prime minister, Binyamin Netanyahu, and his Likud party.
In 2007, Mr Peres was elected president, and he held that role until 2014.
The 93 year-old's health had been in decline this year.
He suffered a minor heart attack in January and was fitted for a pacemaker earlier this month.
Over the past few years, he had dedicated much of his time to working on relations between Israel, the Palestinians and the Arab world through his Peres Centre for Peace.
"I'm sure I shall see peace in my lifetime, even if I have to extend my life for a year or two...", he laughed. "I won't hesitate."
But it was a wish that eluded him.
