The 93-year-old died in his sleep at around 3:00 am (0000 GMT), Rafi Walden, who is also Peres’s son-in-law, told AFP.
He had been surrounded by family members, a source close to Peres told AFP.
His family held a press conference later in the morning, praising Peres’s tireless work ethic and what they called his devotion to peace.
“He had no interest other than serving the people of Israel,” said his son Chemi, his eyes moist as he read a letter on behalf of the family at the hospital.
US President Barack Obama immediately hailed Peres as a friend who “never gave up on the possibility of peace.”
“There are few people who we share this world with who change the course of human history, not just through their role in human events, but because they expand our moral imagination and force us to expect more of ourselves,” Obama said in a statement.
“My friend Shimon was one of those people.”
Former US president Bill Clinton, who helped usher in the Oslo peace accords of the 1990s, said: “The Middle East has lost a fervent advocate for peace and reconciliation.
“I’ll never forget how happy he was 23 years ago when he signed the Oslo accords on the White House lawn, heralding a more hopeful era in Israeli-Palestinian relations.”
Israeli Prime Minister Benjamin Netanyahu expressed his “profound sadness”. Opposition leader Isaac Herzog, the head of Labour, Peres’s longtime party, said he will be “forever remembered as an icon of Israel’s history.”
Peres held nearly every major office in the country, serving twice as prime minister and also as president, a mostly ceremonial role, from 2007 to 2014.
He won the 1994 Nobel Peace Prize jointly with prime minister Yitzhak Rabin and Palestinian leader Yasser Arafat for his role in negotiating the Oslo accords, which envisioned an independent Palestinian state.
The former hawk turned dove was widely respected both in Israel and abroad.
Active in old age
Peres had been in hospital near Tel Aviv since September 13, when he was admitted feeling unwell and suffered the stroke with internal bleeding. He had been under sedation and on respiratory support in intensive care.
But there were signs of improvement last week, and on September 18 Peres’s office said doctors planned to gradually reduce his sedation and respiratory support to judge his response.
Walden had said at the time that Peres had seen “very slow, moderate improvement”.
But on Tuesday a source said his condition had taken a downturn and he was “fighting for his life”. Family members arrived at the hospital.
In January, Peres was hospitalised twice because of heart trouble.
In the first case, the hospital said he had suffered a “mild cardiac event” and underwent catheterisation to widen an artery.
He was rushed to hospital a second time just days later with chest pains and an irregular heartbeat.
Peres had sought to maintain an active schedule despite his age, particularly through events related to his Peres Center for Peace.
When leaving hospital in January, Peres said he was keen to get back to work.
“I’m so happy to return to work, that was the whole purpose of this operation,” he said.
In March, he met British supermodel Naomi Campbell at his Peres Center for Peace during an event linked to International Women’s Day. On the same day, he met visiting US Vice President Joe Biden.
Born in Poland in 1923, Peres emigrated to what was then British-mandated Palestine when he was 11.
He joined the Zionist struggle and met David Ben-Gurion, who would become his mentor and Israel’s first prime minister.
Peres became director general of the nascent defence ministry at just 29.
Beyond his accomplishments in the public eye, he was also seen as a driving force in the development of Israel’s undeclared nuclear programme.
Peres once confided that the secret to his longevity was daily exercise, eating little and drinking one or two glasses of good wine.