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Tens of thousands of South Sudanese have watched the raising of the new country's flag at an independence ceremony in the capital, Juba.
Salva Kiir signed the constitution and took his oath of office in front of the jubilant crowds, becoming the president of the world's newest nation.
Sudan's President Omar al-Bashir and UN chief Ban Ki-moon are among dignitaries watching the historic events.
Sudan earlier became the first state to officially recognise its new neighbour.
The world's newest nation was born at midnight local South Sudanese time (2100 GMT), the climax of a process made possible by the 2005 peace deal that ended a long civil war.
The south's independence follows decades of conflict with the north in which some 1.5 million people died.
South Sudan became the 193rd country recognised by the UN and the 54th UN member state in Africa.
Tears Celebrations in Juba began at midnight (2100 GMT). A countdown clock in the city centre reached zero and the new national anthem was played on television.
Saturday's independence ceremony is being held at the mausoleum of the late rebel leader John Garang, who died just months after signing the peace deal that ended Africa's longest-running conflict.
The BBC's Will Ross in Juba says people have flocked to the event on a baking hot day - some of them climbing trees to get a view.
There is a heartfelt display of excitement mixed with relief that after many years of feeling oppressed the tie with the north has finally been cut, he says.
The Speaker of the South Sudan Legislative Assembly, James Wani Igga, read out the Proclamation of the Independence.
Crowds then cheered as Sudan's national flag was lowered and the new flag of South Sudan was raised as trumpets played the new national anthem.
Afterwards the master of ceremonies told the crowd that President Kiir has decided not to hand over the flag of the Republic of Sudan.
"It shall be kept be kept in the archives of South Sudan in recognition of the common history that we have lived together," he told the crowd.
Our reporter says people in the crowds have been saying it is a moment to celebrate but they are also talking about the many lost relatives who died during the war.
'Southern brothers' Earlier, Mr Bashir arrived at Juba airport where he was greeted by Mr Kiir.
Other dignitaries attending the celebrations include former US Secretary of State Colin Powell and the US permanent representative to the UN, Susan Rice.