His defence minister, armed forces chief General Abdel Fattah al-Sisi, announced Morsi's overthrow on state television, even as police began rounding up key Morsi aides and leaders of the Muslim Brotherhood.
Warrants have been issued for the arrest of a total of 300 Brotherhood officials, state media reported.
The news that Morsi had been forced out drew a rapturous reception from thousands of protesters camped out on the streets of Cairo for days, some of whom celebrated with fireworks.
Fireworks light the sky moments after Egypt's military chief says the president is replaced by chief justice of constitutional court outside the presidential palace in Cairo, Egypt. (AP Photo)
But at least seven of Morsi's supporters were killed in clashes with security forces in Alexandria and the eastern city of Marsa Matrouh, security officials said.
Already this last week, at least 50 people have died in clashes between the Islamist's supporters and opponents in the days leading to his ouster.
Morsi and his senior aides were placed "under house arrest" in a military facility, a senior Muslim Brotherhood member told AFP.
The ousted president was later taken to the defence ministry, Gehad El-Haddad added. His father, Essam El-Haddad, a senior Morsi aide, is one of those detained.
Morsi issued a defiant call for his supporters to defend his elected "legitimacy" in a prerecorded speech that appeared online after Sisi's statement.
Thousands of his supporters remained camped out in northern Cairo, but Egyptian television stations stopped broadcasting live feeds of the pro-Morsi rally after the military announced his overthrow.
US President Barak Obama said he was "deeply concerned" over Morsi's ouster and called on the army to refrain to "arbitrary arrests" of Morsi and his supporters.
In May, Washington approved $1.3 billion in military aid to Egypt. That was now under review, said Obama, as he called for a swift return to democratic rule.
Police also began arresting leaders of Morsi's Muslim Brotherhood movement, an interior ministry general told AFP. Saad al-Katatni, head of Morsi's Freedom and Justice Party was already in custody , he added.
In his speech, Sisi laid out details of the roadmap for a political transition.
The Islamist-drafted constitution would be frozen and presidential elections held early, he said, without specifying when.
The armed forces, which had deployed troops and armour across the country, would "remain far away from politics," he stressed. In the streets of Cairo, the response was immediate.
Tens of thousands of people took to the streets of the capital to celebrate, cheering, whistling, letting off firecrackers and honking car horns in several hours of celebrations.
Army soldiers stand guard in front of protesters who are against Egyptian President Mohamed Morsi, near the Republican Guard headquarters in Cairo. (Reuters photo)
"It's a new historical moment. We got rid of Morsi and the Muslim Brotherhood," said one celebrator, Omar Sherif.
In an amateur video posted online, Morsi declared: "I am the elected president of Egypt" and urged people to "defend this legitimacy".
Earlier, Morsi's national security adviser Essam al-Haddad, said on Facebook: "For the sake of Egypt and for historical accuracy, let's call what is happening by its real name: military coup."
But the opposition Congress Party of Amr Mussa insisted "this is not a coup".
"Consultations will start from now, for a government and reconciliation," said the former Arab League chief, who last year ran unsuccessfully against Morsi for the presidency.
Morsi, Egypt's first freely elected president, came under massive pressure in the run-up to Sunday's anniversary of his maiden year in office. His opponents accused him of failing the 2011 revolution by concentrating power in the hands of his Muslim Brotherhood.
His year in power was marked by a spiralling economic crisis, shortages in fuel and often deadly opposition protests. The embattled 61-year-old had proposed a "consensus government" as a way out of the crisis, the worst since the 2011 uprising that ended three decades of authoritarian rule by Hosni Mubarak.
Female protesters against Egyptian President Mohamed Mursi hold up shoes during a gathering at Tahrir Square in Cairo. (Reuters photo)
But it failed to satisfy his critics and the army stepped in. Its commander named the head of the Supreme Constitutional Court, Adly al-Mansour, as interim leader of the Arab world's most populous country.
Mansour, a previously little known judge, is expected to be sworn in on Thursday.
Opposition leader Mohamed ElBaradei, former head of the UN nuclear watchdog, sat beside army chief Sisi as he announced on state television that Morsi's rule was over.
So too did the heads of the Coptic Church and Al-Azhar, Sunni Islam's highest seat of learning.
The choreography was designed to show broad civilian support for the military's move against Morsi. It was a heavy blow to Morsi's supporters, who a year ago saw his election as president one of the key achievements of the 2011 revolution.
Already, the security forces had shut down broadcasts from a Muslim Brotherhood television channel, a Morsi aide told AFP. Staff of Al-Jazeera's Egyptian affiliate were also arrested after the channel aired a defiant speech by the deposed president, the station reported.
Dozens of armoured personnel carriers headed towards Islamist gatherings around Cairo to head off trouble. But in Cairo's Tahrir Square, the security forces looked on as tens of thousands of anti-Morsi protesters celebrated, dwarfing the pro-Morsi rally in Nasr City, on the opposite side of the capital.
The crowd swelled at nightfall, after a scorching day that saw police officers hand out water to the demonstrators in Tahrir Square, epicentre of the 2011 uprising.ElBaradei.
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