Top judge Adli Mansour, who took the oath hours after a military coup, praised the armed forces and Egyptian people, saying the protests embodied “the nation’s conscience, its ambitions and hopes.”
Morsi was taken to the defence ministry while his "entire presidential team" has been detained, a Muslim Brotherhood spokesman claimed.
Arrest warrants have been issued for 300 leaders and members of Morsi’s Islamist party, according to local reports.
The upheaval comes after days of mass rallies against Egypt's first democratically-elected leader, who army chiefs say had "failed to meet the demands of the people".
In a ceremony broadcast live on state TV today, Mansour – the chief justice of Egypt’s Supreme Constitutional Court – said the era of "worship of the ruler" should end.
He praised the massive street demonstrations that led to Morsi’s ousting and hailed the youth behind the protests that began on June 30. Mansour said: “The most glorious thing about June 30 is that it brought together everyone without discrimination or division. “I offer my greetings to the revolutionary people of Egypt.”
Deposed Morsi, who came to power a year ago, took to FACEBOOK just minutes after military leaders booted him from power to denounce the dramatic developments as “a full military coup”.
In his statement, he said he “totally rejected” his overthrow by the army, which has suspended the country’s constitution and called for early elections.
He also asked Egyptian citizens, both civilians and military, to “abide by the constitution and the law and not to respond to this coup”.
It was unclear if Morsi had access to his own Facebook page or if it was posted by an aide.
Last night Britain's Foreign and Commonwealth Office recommended against all but essential travel to Egypt by Brits.
Hundreds of thousands of Egyptians took to the streets in jubilation following a week of bloody protests in which 50 died.
Green lasers replaced guns in Cairo, sending beams of light into the sky from central Tahrir Square, which was packed with cheering protesters.
Demonstrators had accused Morsi and the Muslim Brotherhood of pursuing an Islamist agenda and of failing to tackle Egypt's economic problems.
Elsewhere in the capital, Islamist supporters of Morsi reacted angrily, shouting: “No to military rule.”
Others chanted: “Islam is coming! We will not leave!”
Opponents and supporters of Morsi also clashed in the Mediterranean city of Alexandria, where at least one person was killed and 50 injured as gunfire broke out. Four of Morsi supporters died in fighting with security forces in the town of Mersa Matruh 100 miles west.
An influential Egyptian Salafist movement, Dawa Salafiya, called on Islamists to leave the streets and go home and urged “all sons of the Islamist movement” not to put themselves in danger and to understand the “reality of the change that is happening in the political situation”.
Egypt’s Muslim and Christian clerics backed the army-sponsored roadmap, which replaces President Morsi of the Muslim Brotherhood with the chief justice of the Supreme Constitutional Court, and appoints a temporary government of technocrats.
Coptic Church head Pope Tawadros II said the plan offered a political vision and would ensure security for all Egyptians.
Liberal opposition leader Mohamed ElBaradei also threw his weight behind it, declaring the Arab Spring revolution of 2011 had been relaunched.
Army chiefs played down fears of a prolonged military dictatorship, assuring the US that they were not interested in long-term rule, said sources.
They have pledged to put a civilian government in place quickly and said they will take steps to ensure the safety of diplomatic missions in Egypt, US officials said. But Washington announced last night that non-essential diplomats and embassy families would leave Egypt amid the unrest.
A Foreign Office spokesman said Brits “should consider whether they have a pressing need to remain”.
He added they “should stay close to home or their hotel, and keep a low profile”.
The Red Sea resorts most popular with Brits are hundreds of miles from Cairo and have not seen protests.