Salva Kiir took the oath as president.
Sudan's President Omar al-Bashir attended and called on the US to end sanctions against his country.
US President Barack Obama said in a statement he was "proud to declare that the United States formally recognises the Republic of South Sudan as a sovereign and independent state upon this day, July 9 2011".
He said: "A proud flag flies over Juba and the map of the world has been redrawn. These symbols speak to the blood that has been spilled, the tears that have been shed, the ballots that have been cast, and the hopes that have been realised by so many millions of people."
At the sceneA sea of people filled Freedom Square in Juba, next to the mausoleum of the late John Garang, the rebel leader who led the South Sudanese during the civil war. They waved flags and screamed in happiness as South Sudan officially became with world's newest nation.
The wild crowds surged forward, dancing for hours in the baking sun. Several people fainted in the heat but the mood was ecstatic. When the giant flag of South Sudan rose on the 30m flagpole, men cried, women ululated and thousands waved flags in a blur of colour.
A host of world leaders spoke on the podium, but the real party was at the back of the site where thousands danced to traditional drum beats.
He added: "We call on US President Barack Obama to deliver on his commitment he announced to lift the unilateral sanctions on Sudan to open to way to normalise his country's relations with Sudan."
Mr Obama indicated more work needed to be done, particularly in the disputed border regions of Abyei and Southern Kordofan.
UK Prime Minister David Cameron issued a statement recognising South Sudan, saying: "This is an historic day, for South Sudan and the whole of Africa."
Russian President Dmitry Medvedev sent a telegram of congratulation and China's special envoy sent President Hu Jintao's "warmest congratulations".
South African President Jacob Zuma said: "We have always aspired to witness the dawn of peace, security and stability prevailing in the whole of the Sudan. That dream is coming to fruition."
'Hearts and minds' The BBC's Will Ross watched the independence ceremony in Juba, saying the euphoria built as people waved goodbye to the north of Sudan and the flag of South Sudan was raised.
South SudanFacts and figures:
- Population: 7.5-9.7 million
- Size: 619,745 sq km (239,285 sq miles), larger than Spain and Portugal combined
- Major languages: English, Arabic (both official), Juba Arabic, Dinka
- Religion: Traditional and a Christian minority
- Main export: Oil
- One of world's least developed countries: Worst maternal mortality rate; most children below 13 not in school; 84% of women are illiterate
- Relations with Sudan: Dividing debts and oil; border disputes; citizenship
- Security: At least seven active rebel groups
The South's independence follows decades of conflict with the north in which some 1.5 million people died.
Saturday's independence ceremony was held at the mausoleum of the late rebel leader John Garang, who died just months after signing the peace deal with Mr Bashir that ended Africa's longest-running conflict.
Meanwhile, in Khartoum, for most people it has been a low-key day, the BBC James Copnall reports from the northern capital.
However, scores of men gathered near the Blue Nile holding giant Sudanese flags and shouting: "Allahu Akbar [God is great]."
Under the Comprehensive Peace Agreement, a referendum was held on independence, which was approved by more than 99% of voters.
South Sudan is rich in oil, but is one of the least developed countries in the world, where one in seven children dies before the age of five.
Fears of a new war resurfaced after recent fighting in Abyei and South Kordofan, where some 170,000 people have been forced from their homes.
Separate deals - and the withdrawal of rival forces from the border - have calmed tensions.
But the two sides must still decide on issues such as drawing up the new border and how to divide Sudan's debts and oil wealth.
Citizenship is also a key sticking point. A new law passed by the National Assembly in Khartoum has withdrawn Sudanese citizenship from all southerners.