Adly Mansour, head of the country's Supreme Constitutional Court, was sworn in Thursday as interim president in Cairo.
At the ceremony, Mansour said the Egyptian people had given him the authority "to amend and correct" the revolution that toppled Hosni Mubarak in 2011.
Until new elections, to be held at an unspecified date, Mansour will have the power to issue constitutional declarations, El-Sisi said.
The Egyptian military has dominated the country for six decades and took direct power for a year and a half after Mubarak's ouster.
Morsy's approval ratings plummeted after his election in June 2012 as his government failed to keep order or revive Egypt's economy.
Morsy's opponents accused him of authoritarianism and forcing through a conservative agenda, and on Monday the military gave him 48 hours to order reforms.
As the deadline neared Wednesday, he offered to form an interim coalition government to oversee parliamentary elections and revise the constitution, which was enacted in January. But those actions failed to satisfy the generals.
The army's move against Morsy and the Muslim Brotherhood, the long-repressed political movement that propelled him to office, provoked wildly conflicting reactions.
In Tahrir Square, the epicenter of two Egyptian upheavals, a vast gathering of Morsy's opponents erupted in jubilation and fireworks at El-Sisi's announcement Wednesday night.
"The crowd walked up to the barricades and started banging on them using rocks, sticks and even bare hands," said Sultan Zaki Al-Saud in a CNN iReport. "It sounded like thunder as the hollow barricades rang with every blow."
During his time in office, Morsy had squared off against Egypt's judiciary, the media, the police and even artists.
Egyptians are frustrated with rampant crime and a struggling economy. Unemployment remains high, food prices are rising and there are frequently electricity cuts and long fuel lines.
'The world is looking'
Morsy had remained defiant.
"The world is looking at us today," he said Wednesday in a taped statement delivered to the Arabic satellite network Al Jazeera. "We by ourselves can bypass the obstacles. We, the sons of Egypt, the sons of this country -- this is the will of the people and cannot be canceled."
Shortly after Morsy's statement aired, Al Jazeera reported its Cairo studios had been raided during a live broadcast and 28 staff members arrested. Most were later released, it said.
On Thursday, Al Jazeera's acting chief, Mostefa Souag, demanded the immediate release of the Egyptian channel's managing director, Ayman Gaballah, and Al Jazeera Arabic broadcast engineer Ahmad Hasan.
"A return to Mubarak-era practices of mass arrests and politically motivated imprisonment of Muslim Brotherhood leaders will have the worst possible effect on Egypt's political future," said Human Rights Watch, the U.S.-based advocacy group.
Concerns of a backlash