The election of Mohammed Mursi of the Muslim Brotherhood as Egypt's first freely-chosen president has been hailed around the world.
Islamists say they see Mr Mursi's win as proof the Arab Spring revolution is on the march.
Nile TV reported Field Marshal Hussein Tantawi, leader of the Supreme Council of the Armed Forces, has congratulated Mr Mursi on his victory.
The United States said it welcomed the result, but expects Mr Mursi to ensure stability and not to veer to extremes. A statement issued by the White House said:
We believe it is essential for the Egyptian government to continue to fulfil Egypt's role as a pillar of regional peace, security and stability.
British Foreign Secretary William Hague said the election marked an historic moment for Egypt.
Iran paid tribute to those it called the martyrs of the Egyptian revolution, whom it said were responsible for ushering in a splendid vision of democracy.
Israeli Prime Minister Benjamin Netanyahu said he hoped the peace treaty between the two countries would continue.