Omar Suleiman, the vice-president, announced in a televised address that the president was "waiving" his office, and had handed over authority to the Supreme Council of the Armed Forces.
Suleiman's short statement was received with a roar of approval and by celebratory chanting and flag-waving from a crowd of hundreds of thousands in Cairo's Tahrir Square, as well by pro-democracy campaigners who attended protests across the country on Friday.
The crowd in Tahrir chanted "We have brought down the regime", while many were seen crying, cheering and embracing one another.
Mohamed ElBaradei, an opposition leader, hailed the moment as being "a dream come true" while speaking to Al Jazeera.
"I can't tell you how every Egyptian feels today," he said. "We have been able to restore our humanity ... to be free and independent".
He reiterated that Egypt now needs to return to stability, and proposed that a transition government be put in place for the next year. The government, he said, would include figures from the army, from the opposition and from other circles.
"We need to go on ... our priority is to make sure the country is restored as a socially cohesive, economically vibrant and ... democratic country," he said.
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"Tonight, after all of these weeks of frustration, of violence, of intimidation ... today the people of Egypt undoubtedly [feel they] have been heard, not only by the president, but by people all around the world," our correspondent at Tahrir Square reported, following the announcement.
"The sense of euphoria is simply indescribable," our correspondent at Mubarak's Heliopolis presidential palace, where at least ten thousand pro-democracy activists had gathered, said.
"I have waited, I have worked all my adult life to see the power of the people come to the fore and show itself. I am speechless." Dina Magdi, a pro-democracy campaigner in Tahrir Square told Al Jazeera.
"The moment is not only about Mubarak stepping down, it is also about people's power to bring about the change that no-one ... thought possible."
In Alexandria, Egypt's second city, our correspondent described an "explosion of emotion". He said that hundreds of thousands were celebrating in the streets.
Responding to the announcement, Catherine Ashton, the European Union's foreign policy chief, told Al Jazeera that the 27-nation bloc "respect[ed] the decision that President Mubarak has taken".
She said the EU wanted to "pay tribute to the dignity of" Egyptians' behaviour at this time, and that Europe was ready to offer its assistance in this transition period in the fields of elections, building civil society and other areas.
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