Egyptian President Hosni Mubarak has resigned following 18 days of protests that saw hundreds of thousands of people take to the streets of Cairo.
Vice-President Omar Suleiman has named the Supreme Council of the Armed Forces to run the country's affairs, state television said.
'Taking into consideration the difficult circumstances the country is going through, President Mohammed Hosni Mubarak has decided to leave the post of president of the republic and has tasked the Supreme Council of the Armed Forces to manage the state's affairs,' Mr Suleiman said.
A ruling party official said that Mubarak and his family had now left Cairo for the Red Sea resort of Sharm el-Sheikh where there is a presidential residence.
US President Barack Obama said that the world had witnessed a true moment of history.
'Egyptians have inspired us,' Mr Obama told reporters at the White House.
'Egyptians have made it clear that nothing less than genuine democracy will carry the day,' Mr Obama also said, praising the military for serving responsibly to preserve the state.
The armed forces would now have to ensure a political transition that was 'credible in the eyes of the Egyptian people,' Mr Obama said, warning there could be 'difficult days ahead'.
US Vice-President Joe Biden said the change of power in Egypt was a 'pivotal' moment in history for that country and the Middle East. He said the transition must be irreversible.
As news spread cries of 'Allahu Akbar' - God is greatest! - and howls of victory rang out in the streets of the capital and firecrackers exploded.
Egyptians waved flags, cried, cheered and embraced in celebration as the resignation. 'The people have brought down the regime,' 'chanted the crowds in Tahrir Square.
'The greatest revolution of the world is unfolding here,'
Elsewhere in Cairo, cars honked their horns and fireworks went off as Egyptians celebrated the end of Mubarak's reign.
EU Foreign Policy Chief Catherine Ashton has said she respects Mr Mubarak's decision to stand down and called for dialogue for the formation of a broad-based government.
'Egypt listened to the voices of the Egyptian people. The future of Egypt rightly remains in the hands of the Egyptian people.'
British Prime Minister David Cameron said Egypt now has a moment of opportunity.
French President Nicolas Sarkozy urged Egypt to now take steps towards free elections.
'France ardently hopes the new Egyptian authorities will take steps that lead to establishment of democratic institutions through free and transparent elections,' Mr Sarkozy said in a statement issued by his Élysée Palace office.
ElBaradei hails 'greatest day'
Egyptian opposition figure Mohamed ElBaradei said it was the ‘greatest day’ of his life.
‘We have waited for this day for decades. We all look forward to working with the military to prepare for free and fair elections. I look forward to a transitional period of co-sharing of power between the army and the people,’ Mr ElBaradei told Reuters by telephone.
Asked if he was going to run for the presidency, Mr ElBaradei said: ‘The issue is not on my mind. I have lived enough and am happy to see Egypt liberated.’