In his first address as the President of the new South Sudan Republic, Mr Salva Kiir asked the people of the South Sudan to forgive but not forget those who committed atrocities against them during decades of conflict with the north in which some 1.5 million people died.
Mr Kiir, who signed the constitution and took his oath of office in front of a jubilant crowd, said South Sudan faces a number of challenges, ranging from conflict, poverty and economic hardships.
"It's important for us to note that this land has seen many sufferings and deaths," Mr Kiir said, adding, "It is also important for us to forgive, though we shall not forget...we have been at the receiving end of injustice for the past decades."
Tens of thousands of South Sudanese watched the raising of the new country's flag at an independence ceremony in the capital, Juba. Mr Kiir signed the constitution and took his oath of office in front of jubilant crowds as president of the world's newest nation.
The independence ceremony was 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.
President of Sudan Omar Hassan al-Bashir, who agreed the 2005 peace deal with the Sudan People's Liberation Army (SPLA), also spoke at the ceremony.
"We congratulate our brothers in the south for the establishment of their new state," Reuters news agency quotes him as saying.
The under-developed oil-producer won its independence in a January referendum and Salva Kiir stood next to his old civil war foe, President Bashir.
The US and Britain announced their recognition of South Sudan as a sovereign nation. President Barack Obama said the day was a reminder that "after the darkness of war, the light of a new dawn is possible."
"A proud flag flies over Juba and the map of the world has been redrawn," Obama said in a statement. "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 realized by so many millions of people."
Dignitaries including U.N. Secretary General Ban Ki-moon and the leaders of about 30 African nations, including Ugandan President Yoweri Museveni attended.