The death of the controversial 85-year-old former army commander - who was admired and despised in equal measure - was announced by his son Gilad at the hospital near Tel Aviv where he had been treated.
Dr Shlomo Noy, spokesman for the Sheba Medical Center, said in the years Sharon had been treated there his condition had been one of "minimal consciousness" and he had suffered "ups and downs".
He added: "His heart weakened and he peacefully departed from his family who were always at his side with love and support."
The veteran soldier, nicknamed The Bulldozer, fought in the series of wars that forged the state of Israel before entering politics in 1973.
Critics held him responsible for the 1982 massacre of hundreds of Palestinians by Israel's Lebanese Phalangist allies in Beirut refugee camps.
However, supporters claimed he made efforts to secure a stable peace as prime minister between 2001 and 2006, including unilateral withdrawal from the Gaza Strip.
Sharon was still in office when he suffered his stroke in April 2006. He never regained consciousness.
Complications after surgery at the beginning of this month led to a sharp deterioration in his condition.
World leaders yesterday paid tribute to Sharon, including UK Prime Minister David Cameron.
"Ariel Sharon is one of the most significant figures in Israeli history and as prime minister he took brave and controversial decisions in pursuit of peace, before he was so tragically incapacitated," he said. "Israel has today lost an important leader."
The official spokesman for Israeli prime minister Benjamin Netanyahu said on Twitter: "Ariel Sharon's memory will be enshrined forever in the heart of the nation."
US President Barack Obama said he and his wife, Michelle, sent their deepest condolences to Sharon's family and to Israelis on "the loss of a leader who dedicated his life to the state of Israel".
Russian President Vladimir Putin praised Ariel Sharon's "personal qualities and his activities to protect Israel's interests, noting a high respect for him among compatriots and his high authority in the international arena", the Kremlin said.
A spokesman for German Chancellor Angela Merkel said: "With his courageous decision to withdraw the Israeli settlers from the Gaza Strip, he took a historic step on the path to a deal with the Palestinians and a two-state solution."
Palestinians accused Sharon of sparking their second intifada - uprising against Israeli occupation - with a provocative visit to the al Aqsa mosque plaza in Jerusalem's Old City in 2000.
He further embittered them with a crushing army sweep of self-rule areas of the West Bank in 2002 after a wave of Palestinian suicide bombings, and his siege of Palestinian leader Yasser Arafat in his Ramallah compound.
But he surprised many by withdrawing soldiers and settlers from Gaza in 2005 under a policy of "disengagement" from conflict and dialogue with the Palestinians.
The pullout, however, led to Gaza's takeover by the Palestinian Hamas Islamists.
The Hamas leadership, unlike the West Bank-based president Mahmoud Abbas, spurns co-existence with Israel.
Palestinians in Gaza were yesterday handing out sweets to passers-by and motorists in celebration of Sharon's passing.
"We have become more confident in victory with the departure of this tyrant [Sharon]," said Hamas spokesman Sami Abu Zuhri.
"Our people today feel extreme happiness at the death and departure of this criminal whose hands were smeared with the blood of our people and the blood of our leaders here and in exile."
Sharon was married twice. His first wife, Margalit, died in a car accident in 1962.
They had one son, who was killed in 1967 when a friend accidentally shot him while playing with a rifle.
In 1963, Sharon married Margalit's sister, Lily, who died of cancer in 2000. They had two sons.
Officials yesterday said Sharon would be buried in a state funeral to which foreign dignitaries would be invited.