Mr Mubarak ruled for 30 years, suppressing dissent and protest, and jailing opponents.
US President Barack Obama said that Egypt must now move to civilian and democratic rule.
This was not the end but the beginning and there were difficult days ahead, the US president added, but he was confident the people could find the answers.
"The people of Egypt have spoken, their voices have been heard," Mr Obama said. "Egypt will never be the same again."
"They have made it clear that nothing less than genuine democracy will carry the day."
'Historic change' 重要的歷史轉捩點＆世界其他強權對此事件之反應
There was jubilation throughout the Middle East and North Africa, including in Tunisia, where people overthrew their own president last month.
For the Arab League, Mr Moussa said events in Egypt presented an opportunity to build a national consensus.
Meanwhile, Iran described the recent events as a "great victory".
A senior Israeli official expressed the hope that Mr Mubarak's departure would "bring no change to its peaceful relations with Cairo".
UN Secretary General Ban Ki-moon said he respected the "difficult decision" taken in the people's interests, and called for an "orderly and peaceful transition".
European Union leaders reacted positively to the news of Mr Mubarak's resignation.
Foreign policy chief Baroness Ashton said the EU "respected" the decision.
"It is important now that the dialogue is accelerated leading to a broad-based government which will respect the aspirations of, and deliver stability for, the Egyptian people," she said.
UK Prime Minister David Cameron said this was a "really precious moment of opportunity to have a government that can bring the people together", and called for a "move to civilian and democratic rule".
German Chancellor Angela Merkel welcomed the "historic change" in Egypt.
US Vice-President Joe Biden said Egypt had reached a pivotal moment in history.
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