Mansour was sworn in before fellow judges at the country's Supreme Constitutional Court.
During the swearing-in ceremony, Mansour praised those who took part in massive demonstrations as protestors on both sides continued to make their presence known in Cairo.
According to military decree, Mansour will serve as Egypt's interim leader until a new president is elected. A date for that vote has yet to be set. But Mansour has the authority to declare new laws during the transition.
The swearing-in ceremony comes after Egyptian security officials revealed that the supreme leader of the Muslim Brotherhood had been arrested and flown to Cairo on a military helicopter.
The officials said Mohammed Badie was arrested Wednesday night in a coastal city west of Cairo not far from the Libyan border. He had been staying in a villa owned by a businessman with Brotherhood links.
Badie is on a wanted list of more than 200 Brotherhood officials and leaders of other Islamist groups.
Ousted President Mohammed Morsi was a longtime leader of the Brotherhood.
The Egyptian military ousted Morsi on Wednesday. Morsi, who a year ago became Egypt's first freely elected president, has been under house arrest at an undisclosed location since the generals pushed him out in what his supporters have decried as a military coup. At least a dozen of his advisers and aides are also under house arrest.
Meantime, other members of the party are facing murder charges in connection with the death of protestors.
It was those massive street protests that brought Cairo and the country to a stop. Supporters and opponents of ousted President Mohamed Morsi took to the streets Thursday. The demonstrations continued following the Egyptian military's decision to remove the democratically elected president. Morsi backers say it was the wrong approach.
"It's our right. It's the people's right to choose who rules them and to choose their constitution," said Sarah El-Fathy, a Morsi supporter.
The Muslim Brotherhood and Morsi call his removal a military coup."We put full responsibility on every person that participated in that coup and empowered it to happen," said Essam El Haddad, Morsi's Foreign Relations Advisor.
Egyptians in the U.S. have mixed feelings about the military stepping in and removing the man elected by the people just a year ago.
"I want to be optimistic and hopeful but I also know the military is not the most trustworthy entity in Egypt as well," said Mohamed Abdelgany, an Egyptian American.
Egypt is a longtime key ally to the U.S., and that is complicating how the White House responds to the change in leadership.
President Barack Obama issued the following statement:
"We are deeply concerned by the decision of the Egyptian Armed Forces to remove President Morsi and suspend the Egyptian constitution. I now call on the Egyptian military to move quickly and responsibly to return full authority back to a democratically elected civilian government as soon as possible."
The White House is being careful not to use the word "coup" to describe the change in leadership in Egypt.
U.S. law would require the administration to suspend aid to Egypt under that scenario. Egypt gets about $1.5 billion a year from the U.S.
Even with an interim leader now in place, Egypt remains on an uncertain course following Morsi's ouster, and the possibility of further confrontation still looms. Beyond the fears over violence, some protesters are concerned whether an army-installed administration can lead to real democracy.
The world is watching to see how Egypt handles this period of uncertainty.
"What we need to happen now in Egypt is for democracy to flourish and for a genuine Democratic transition to take place," said British Prime Minister David Cameron.
The Muslim Brotherhood says it will not work with the new leadership and has told followers to continue protesting peacefully. Elections are expected in the next nine months to a year.
The Associated Press contributed to this report.
