In announcing Mubarak's resignation on state television, Vice President Omar Suleiman said the out-going leader designated the military council to run the republic.
"In these grave circumstances that the country is passing through, President Hosni Mubarak has decided to leave his position," Suleiman said through a translator.
Anti-government protesters have been demonstrating since Jan. 25, calling for Mubarak's resignation, among other things.
The military council -- which earlier Friday said it would lift the state of emergency that has stifled judicial rights and civil liberties -- is made up of the defense minister, the military chiefs of staff and operation, and commanders of the country's armed forces, Fox News said.
Al-Jazeera reported people fainted in the streets after hearing the news around 6 p.m. local time.
State television also backed off its criticisms of foreign influences on the anti-government demonstrations, CBS said.
Mubarak left Cairo for his estate in the Red Sea resort community of Sharm el-Sheik, ABC News reported.
"Welcome back, Egypt," activist and Google marketing executive Wael Ghonim told CNN. "To President Mubarak and all those who thought being in power means you can oppress people -- at the end of the day we have a choice. … Today is a day of celebration."
"We are dreamers and we made it happen," Ghonim said, noting he was at his mom's house when he heard the news.
Mubarak was responsible for the deaths of 300 "innocent Egyptians" during the protests, Ghonim said.
"In the history books, there will be one word to describe you: dictator," he said.
In a speech Thursday, Mubarak reiterated his intention to remain in office but not seek re-election, angering anti-government demonstrators who have been protesting since Jan. 25. Among other things, the protesters want the 82-year-old president to end his 30-year rule.
U.S. Vice President Joseph Biden, in an appearance in Kentucky, called Friday's developments historic and pivotal.
Demonstrators gathered at Cairo's Tahrir Square, considered ground zero for the protests, as part of a multi-site, multi-city "Friday of Martyrs" rally to memorialize the more than 300 people killed since the protests started.
Witnesses told al-Masry al-Youm thousands of protesters gathered near the presidential palace, demanding that Mubarak step down. Military vehicles, including tanks, were positioned between the protesters and the palace.
In Suez, witnesses said demonstrators occupied three government buildings after midday prayers, al-Masry al-Youm said.
Meanwhile, the Web site of the ruling National Democratic Party was hacked Friday, al-Masry al-Youm reported.
One message posted by the hackers read, "closed until dropping Mubarak & the regime," which was replaced with, "Protect our country and our beloved Egypt from all enemies and harm, I love you Egypt."