The president planned to swear-in ElBaradei later Saturday, said Khaled Dawoud, an official with the main opposition National Salvation Front.
ElBaradei, a former director of the U.N.'s nuclear watchdog agency, led the protests against President Hosni Mubarak during the Arab Spring uprising that ended his autocratic rule in February 2011.
The revolution also opened the way for the political rise of the Muslim Brotherhood, which was long under pressure from Mubarak's Western-backed regime. Elections last year brought Morsi to the presidency, but ElBaradei remained a voice of dissent, once saying the Brotherhood lived "in a delusion" for thinking its members could manage the country on their own.
Egypt's new president — chief justice of the country's constitutional court — is little-known in international circles. But the choice of the 71-year-old ElBaradei gives the administration and prominent global figure to make its case to Washington and other Western allies trying to reassess policies after what Morsi's backers have described as a "coup." Morsi remains under detention in an undisclosed location.
Earlier, the president held talks with the army chief and interior minister in apparent attempts to work out strategies to contain another round of violence.
Morsi's supporters have vowed to take to the streets until the toppled Islamist leader is reinstated. His opponents, meanwhile, have called for more mass rallies to defend what they call the "gains of June 30."
"The people here and in all of Egypt's squares are ready for martyrdom to restore legitimacy," said Abdullah Shehatah, a senior leader of the Freedom and Justice Party, the Brotherhood's political arm. Speaking at the main sit-in site of Morsi supporters in Cairo, he said: "This coup and all its institutions are illegal."