Mohammed Mursi has been sworn in as the country's first civilian, democratically elected president at a historic ceremony in Cairo.
Mr Mursi, the Muslim Brotherhood's candidate, took the oath before the Supreme Constitutional Court.
He promised to respect the constitution and the rule of law, and to protect the people of Egypt.
He is speaking at Cairo University before going to an army base for the handover from military rule.
In the ceremony before the court, Mr Mursi said the Egyptian people had "laid the foundations for a new life, for full freedom, a genuine democracy, for putting the meaning and significance of the constitution and stability above everything else".
He said his government would be based on the democratic pillars of "the constitutional court, the Egyptian judiciary, and the executive and legislative powers".
There was no mention of the ruling Supreme Council of the Armed Forces (Scaf), which has dissolved parliament and issued sweeping decrees in what many Egyptians have decried as equivalent to a coup.
Mr Mursi's administration may now try to ease the military out, knowing that in overt confrontation, the military is the one with the guns, says regional analyst Magdi Abdelhadi.
But the Mubarak regime is still largely intact and many in it will not work with the new president, he says.
'Free people'
"I swear by almighty God that I will faithfully defend the republican system, and I will respect the constitution and the rule of law, and I will look after people's interests fully, and protect the country's independence and territorial integrity," Mr Mursi said as he was sworn in.
Mr Mursi took his oath of office about an hour later than scheduled at the constitutional court - not as originally planned at the parliament, dissolved by the Scaf last week.
The assembly, elected last November, was dominated by the Muslim Brotherhood-backed Freedom and Justice Party (FJP) and other Islamists.
Mr Mursi said he was determined that the constitutional court would remain "independent, strong, effective - away from any suspicion and abuse.
"It is a free institution in a free land for a free people," he said.
Unlike during the Mubarak days, the traffic was not stopped for Saturday's ceremony - underlining Mr Mursi's wish to be seen as one of the people, says the BBC's Jon Leyne in Cairo.
On Friday, he undertook a symbolic swearing-in before crowds gathered in Tahrir Square to protest the Scaf.
"The revolution must continue until all its objectives are met," Mr Mursi told the crowds.
'Islamic law fears'
Handling relations with the Scaf is likely to be a key test for Mr Mursi as he begins his term of office.
The Scaf had previously said it would hand over power to Mr Mursi by the end of the month.
However, Scaf member Maj Gen Mohamed al-Assar told Egyptian media earlier this week that the head of Scaf, Field-Marshal Hussein Tantawi, would remain as defence minister under Mr Mursi.
Also on Friday, Mr Mursi performed prayers at Cairo's al-Azhar mosque, one of the most prominent seats of learning in Sunni Islam.
He has sought to allay fears among some secular and Coptic Christian Egyptians that he will use his presidency to impose Islamic law.
Mr Mursi's campaign has said he plans to appoint a woman and a Coptic Christian as his vice-presidents.
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