In a statement read out on state TV, they said they had asked the current government to stay on until a new one was formed.
The military also reaffirmed the country's commitment to all its international treaties.
The United States and Israel have welcomed the military's moves.
US President Barack Obama said he "welcomed the historic change that has been made by the Egyptian people".
He also "welcomed the Supreme Council of the Armed Forces' announcement today that it is committed to a democratic civilian transition, and will stand by Egypt's international obligations," a statement released by the White House said.
The announcement, which was read by a senior officer on state TV, implicitly confirms that the country's 1979 peace treaty with Israel will remain intact.
Israeli PM Benjamin Netanyahu also welcomed the announcement, saying the treaty was a cornerstone of Middle East stability.
"The longstanding peace treaty between Israel and Egypt has greatly contributed to both countries and is the cornerstone for peace and stability in the entire Middle East," he said.
Meanwhile the authorities have banned three senior officials close to Mr Mubarak from foreign travel.
The three are former Prime Minister Ahmed Nazif, former Interior Minister Habib al-Adli and current Information Minister Anas al-Fekky.
State TV said the men were under investigation, but no more details were available.
The moves came as thousands of people maintained a presence in Cairo's Tahrir Square, celebrating President Hosni Mubarak's resignation on Friday after 18 days of protests.
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