In a televised address to the nation, Army chief Gen Abdul Fattah al-Sisi said Mr Morsi had "failed to meet the demands of the people".
Fresh presidential and parliamentary elections will be held, he said, announcing the appointment of Mr Mansour and an interim council and a technocratic government until new presidential and parliamentary elections are held.
No details were given about when polls would take place.
Mr Morsi described the actions as a military coup.
He and both the head and deputy chief of the Muslim Brotherhood have been arrested, with warrants issued for 300 members of the political party, according to reports.
World leaders have voiced concerns over the military intervention.
"We are deeply concerned by the decision of the Egyptian Armed Forces to remove President Morsi and suspend the Egyptian constitution," said U.S. President Barack Obama.
EU foreign policy chief Catherine Ashton called for a quick return to democracy.
"I urge all sides to rapidly return to the democratic process, including the holding of free and fair presidential and parliamentary elections and the approval of a constitution," she said.
Mr Morsi's overthrow came after an army deadline for him to step down expired and he refused to yield to mass nationwide demonstrations.
News of the elected Islamist leader's forced exit led to celebrations in Cairo's Tahir Square.
Image: © Getty
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