The council’s communique number five, which was read out on state television, said a transitional period of military rule will last six months while reforms were put in place to allow free elections.
It announced the "dissolution of the lower and upper houses of parliament", which is dominated by the National Democratic Party of former president Hosni Mubarak, thanks to elections in which widespread fraud is said to have taken place.
The council announced the suspension of the constitution and said it would "run the affairs of the country on a temporary basis for six months or until the end of elections."
A committee will also be formed to oversee amendments to the constitution and a popular referendum will be organised to vote on the changes. Restrictions on presidential candidates are expected to be eased.
The statement also confirmed Defence Minister Hussein Tantawi as Egypt's de facto head of state.
The military will define the role of Vice-President Omar Suleiman, who stepped in to effectively replace Mubarak, later.
"The head of the Supreme Council of the Armed Forces will represent the council domestically and internationally," it said, stressing its commitment to international agreements.
Israeli Defence Minister Ehud Barak said Sunday that Mubarak’s fall does not pose a danger to the two countries’ relations.
“I don't think that the relationship between Israel and Egypt is under any risk, or that any kind of operational risk is waiting for us just behind the corner," Barak told ABC's This Week programme.