"Former vice president General Omar Suleiman's health deteriorated suddenly around three weeks ago and he was taken to hospital in Cleveland, Ohio, where he died in the early hours of Thursday," Egypt's state-run MENA news agency said. He was 76.
"It came suddenly while he was having medical tests in Cleveland," Suleiman's aide Hussein Kamal said.
Suleiman was head of Egypt's intelligence services and served as vice president under Mubarak before his ouster.
In a somber, one-minute television announcement in February 2011, Suleiman announced that Mubarak had resigned his post as president after three decades in power and said the Supreme Council of the Armed Forces would run the affairs of the country.
Suleiman had disappeared after the revolution from public eye only to come back as a presidential candidate.
However, his presidential bid was blocked by the Supreme Presidential Electoral Committee (SPEC) because he failed to acquire the number of recommendations stipulated by the election law.
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During Suleiman's short-lived presidential bid he portrayed himself as a staunch enemy of the Muslim Brotherhood and Islamist forces.
In the final years of Mubarak's reign, he was one of the key architects of the blockade of the Gaza Strip.
After Mohammed Mursi, a senior figure in the Brotherhood, became Egypt's president, Suleiman warned that Egypt would become a theocratic state.
Suleiman left Egypt after the failed bid to run in the country's first ever free presidential elections in May.
He first travelled to Dubai but later headed to Germany and then on to the US for treatment, General Saad al-Abbassi, a member of Suleiman's presidential campaign team said.