Mohamed Morsi, the first Islamist to be elected to the Egyptian presidency, has declared he will be a leader "for all Egyptians".
In his first speech since being declared the country's next leader, Mr Morsi called for unity and said he carries "a message of peace" to the world.
"I will be a president for all Egyptians," he said in the televised address.
He paid tribute to nearly 900 protesters killed in last year's uprising, saying without the "blood of the martyrs", he would not have made it to the presidency.
"The revolution continues, until all its demands are met," he said.
Mr Morsi also pledged to preserve Egypt's international accords, a reference to the peace deal with Israel.
But he did not mention the last-minute power grab by the ruling military that stripped the new president of most of his major powers.
The state election committee earlier announced Mr Morsi had narrowly defeated Hosni Mubarak's last prime minister Ahmed Shafiq in a run-off vote.
Mr Morsi, of the long-surpressed Muslim Brotherhood, won 51.73% of the vote.
He clinched 13,230,131 votes to Mr Shafiq's 12,347,380.
On hearing Mr Morsi was their new president, thousands of Muslim Brotherhood supporters burst into cheers at Cairo's Tahrir Square, dancing and waving flags and posters of the Islamist leader.
A retiring individual, Mr Morsi is Egypt's first president since Hosni Mubarak was ousted in a popular uprising last year.
However, the military council, which ruled the Arab nation after Mr Mubarak stood down, earlier this month curbed the powers of the presidency.
The changes mean the head of state will have to work closely with the army on a planned democratic constitution.
Mr Morsi, 60, is a US-educated engineer who spent time in jail under Mr Mubarak.
He won the first round ballot in May with just under a quarter of the vote.
Many Egyptians were dismayed that what was billed as their first democratic presidential election turned into a power struggle between the military and the Muslim Brotherhood - the same forces that faced off under the old regime.
The election, in which more than 50 million voters were eligible to cast their ballot, saw a relatively low turnout of just 51.8%.
Foreign Secretary William Hague said it is "an historic moment for Egypt".
"I congratulate the Egyptian people for their commitment to the democratic process and electing a new president of Egypt," he said.
"I welcome Mr Morsi's statement that he intends to form an inclusive government that governs on behalf of all the Egyptian people.
"Britain will support the Egyptian people and their leaders as they take steps to consolidate their democratic rights and institutions and to reinvigorate the Egyptian economy."