Barack Obama, the US president, said the move was the beginning, not the end, of the transition to democracy in Egypt.
"The people of Egypt have spoken ~ their voices have been heard and Egypt will never be the same," he said on Friday evening.
The US leader added that Egyptians had inspired the world with their moral force and nonviolence, but warned there could be "difficult days ahead".
Earlier, Catherine Ashton, the European Union's foreign policy chief, said it showed Mubarak had "listened the voices of the Egyptian people" and opened the way to reform in the country.
"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 just after Egypt's vice-president delivered the news on Friday. "The future of Egypt rightly remains in the hands of the Egyptian people," she said.
Angela Merkel, the German chancellor, hailed Mubarak's decision as an "historic change", and called on the country to respect its 1979 peace treaty with Israel.
Her sentiments were echoed by a senior Israeli official, who said: "We hope that the change to democracy in Egypt will happen without violence and that the peace accord will remain."
David Cameron, Britain's prime minister, also urged Egypt to "move towards civilian and democratic rule".Meanwhile Switzerland reacted by saying it was freezing the assets potentially belonging to Mubarak, according to a foreign ministry spokesman.
"Egypt now has a really precious moment of opportunity to have a government that can bring the country together," he said.
'LESSON' FOR ARAB NATIONS
The Arab world was quick to respond to Mubarak's resignation, with Amr Moussa, the secretary-general of the Arab League, saying there was now a "big chance" to build a "national censensus" in the coming period.
"There is a big chance now and a window has opened after this white revolution and after the president's concession," he told Al Arabiya television.
said these events were a
"lesson" for other Arab governments..Arab regimes should learn a lesson from what has happened. Mubarak's departure should have happened from the start. It's only natural after his oppression and corruption. Congratulations to our people in Egypt."
Sami Abu Zuhri, A Hamas spokesman, said.
"The resignation of Egyptian president ... is the beginning of the victory of the Egyptian revolution. Such a victory was the result of the sacrifices and the steadfastness of the Egyptian people," he told the Reuters news agency.
"positive, important step towards the Egyptian people's aspirations of achieving democracy and reform and a life of dignity".
'WHERE TO GO NEXT'
Iran said Egyptians had achieved a
"great victory. The conquest by the will of the great Egyptian nation over the resistance and persistence of officials who were dependent on the world powers is a great victory," Ramin Mehmanparast told Al-Alam television.
However analysts have remained cautious despite the scenes of jubilation across Egypt.
"Huge questions remain as to where we go next, and it could be a tortuous path," Julien Barnes-Dacey, a middle-east analyst told the Reuters news agency. "There must be serious questions over how acceptable Suleiman will be given his support for Mubarak. I think he has to come up with sessions very quickly for very comprehensive reform.
"There will be a feeling of jubilation on the streets in the very short term, but I think if they do not seek change protests could still continue."
But in Egypt, opposition figurehead Mohamed ElBaradei said it was the "greatest day" of his life following the announcement. "The country has been liberated".