Egypt’s first democratically-elected president, Mohammed Morsi, will start forming a government, after promising to be a leader for all Egyptians.
World leaders have congratulated the Muslim Brotherhood’s candidate who defeated ex-PM Ahmed Shafiq.
Morsi could be sworn in on 30 June, although questions remain over the extent of his authority.
The ruling military council has taken control of many of the president’s powers and has dissolved parliament.
In his victory speech on Sunday, Morsi, 60, urged Egyptians “to strengthen our national unity” and promised an inclusive presidency.
“There is no room now for the language of confrontation,” he said, after the election authorities declared that he had won 51.73% in the 16-17 June presidential run-off.
Morsi will now have to begin building a civilian administration and the focus will now turn to his choice of prime minister.
The BBC’s Jon Leyne in Cairo said there was some talk of him having discussions with Nobel peace-prize winner Mohamed ElBaradei, which would provide reassurance to non-Islamists.
Morsi has also promised to appoint a range of vice presidents and a cabinet of “all the talents”.
On hearing the news of his victory, tens of thousands of Muslim Brotherhood supporters cheered in Cairo’s Tahrir Square, chanting, “Down with military rule!”
Celebrations continued until the early hours of Monday morning.
Morsi paid tribute to the protesters who died in last year’s uprising against former President Hosni Mubarak but also praised the role of Egypt’s powerful armed forces.
“The revolution goes on, carries on until all the objectives of the revolution are achieved and together we will complete this march” he said.
He also said he would honor international treaties.
Field Marshal Mohamed Hussein Tantawi, Egypt’s military ruler, was among the first to congratulate him on his victory.
But the BBC’s Jon Leyne in Cairo says the question remains how much real power Morsi will have when he swears the oath of office.
He will not have a sitting parliament or a permanent constitution to define his powers or duties.
And the Supreme Council of the Armed Forces (SCAF) which has led Egypt since last year’s revolution has issued a series of recent decrees.
Responding to Morsi’s election, the White House called result “a milestone for Egypt’s transition to democracy”.
Israel responded to his election, saying that it “values the democratic process” and expected to “continue co-operation” with Egypt’s government on the basis of the 1979 peace accord.
UK Foreign Secretary William Hague also congratulated Morsi, saying the election marked “an historic moment for Egypt”.