The swearing in of Mr Mansour comes a day after the military ousted and detained President Mohamed Morsi following a week of widespread demonstrations.
There are reports at least 60 people have been killed in the unrest, and there are calls from countries around the world for an end to the violence and a swift return to democracy in Egypt.
Michael Kenny reports.
In a ceremony broadcast across Egypt, 67-year-old chief justice Adly Mansour was sworn in as the nation's interim president.
He is expected to serve in the role until fresh presidential elections are held at a yet to be determined date.
The swearing in of Mr Mansour is part of a broader political transition in Egypt, set out by the military.
It includes a freeze on the constitution drafted under the Government of Mr Morsi, who was in power for just over a year.
In a ceremony in the Supreme Constitutional Court, Mr Mansour has called on the protesters who helped force Mr Morsi out to push ahead with real political change in Egypt.
"The spirit of the revolution carries to us the hope of adhering to the principles and values of the revolution and, on top of these hopes, to put an end to worshipping the ruler and creating a demigod."
Mr Morsi's presidency unravelled after the Egyptian army gave him a deadline to relinquish power in the face of massive demonstrations against his rule.
The protests were the largest since the 18 days of rallies that preceded the February 2011 resignation of former president Hosni Mubarak.
On that occasion, Mr Mubarak, himself from a military background, handed over power to the military of his own accord.
In the aftermath of the current coup, security forces have rounded up members of Mohamed Morsi's influential Islamist group, the Muslim Brotherhood.
Among those arrested was the group's supreme guide Mohammed Badie.
The arrests have been strongly condemned by a spokesman for the Muslim Brotherhood, Gehad El Haddad.
"We put full responsibility on every person that participated in that coup and empowered it to happen and we put responsibility on them-on anything, any harm happening to the person of the presidency, to the legitimacy of the nation, to Dr Mohammed Morsi and we call on them to momentarily end the illegitimate detainment of the president, of the elected president, between him and his people."
The Muslim Brotherhood, which had been banned under former President Mubarak, came to power after the 2011 uprising.
President Morsi's opponents had accused him of failing to live up to the ideals of the uprising by concentrating too much power in the Brotherhood's hands.
But the ousted president's supporters say he inherited many problems from a corrupt Mubarak government.
They insist he should have been allowed to serve out his term, as Egypt's first democratically elected president, until 2016.
That is the view shared by one demonstrator, named Ahmed, at a rally in support of President Morsi in Cairo.
"I'm an Egyptian citizen and I am not affiliated to any political party. I am out here to defend President Morsi's legitimacy. President Morsi was legitimately elected. The whole world stands witness to this. All of us are here to defend legitimacy, not for the character of President Morsi. I am not part of any political party, but I will not let go of legitimacy, even if it comes at the cost of my blood and the blood of everyone here."
Similar protests have been held across Egypt led by critics of Mohammed Morsi.
They see the ousting of Mr Morsi as a fresh opportunity to install a more democratic government in Egypt.
Former Egyptian Foreign Minister and a Member of the Opposition National Salvation Front, Amr Moussa has told Reuters he believes President Morsi was forced out by the people.
"This was a popular uprising, a popular revolution. In fact, I can say it was a popular impeachment of the president. It didn't start by the action of the army. It didn't come as a result of a meeting between a few (army) officers deciding to do this or that. No - it was the people who insisted that they cannot afford to have another year of failure. The state was about to fail. The state was about to collapse."
Mr Moussa says a critical step to restore democracy now lies in moving towards fresh elections.
That is a view shared by Egypt's Ambassador to Australia, Hassan El Laithy.
He has told SBS there will be real challenges in the months ahead for the country's interim president to try and bridge the divide between supporters and critics of President Morsi.
"This is the time to work. Tis is the time to achieve in good faith and sharing the right values, whether democracy and whether peaceful coexistence to include all parties in a real reconciliatory process in the country."
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