Sharon, 85, had been in a coma since a debilitating stroke eight years ago.
The Sheba Medical Center that has been treating Sharon said last week that his health has been declining.
Sharon had been suffering from failure of his vital organs including his kidneys shortly before his death.
His son Gilad Sharon said: "He has gone. He went when he decided to go."
The hospital treating Sharon said he died about an hour ago.
Hospital spokesman Dr Shlomo Noy said: "The Sheba Medical Center at Tel Hashomer announces with sorrow the death of Mr Ariel Sharon who passed about an hour ago."
He said that during the years Sharon had been treated his condition was defined as "minimal consciousness" and he had had "ups and downs".
"Today his heart weakened and he peacefully departed from his family who were always at his side with love and support."