"The referendum was correct, accurate and transparent and we have no objection to the results," said referendum chairman Mohamed Ibrahim Khalil.
People gathered at former rebel leader John Garang's mausoleum in Juba to watch the ceremony via satellite. More than 1,000 people cheered loudly when the result was announced.
President Omar al-Bashir said earlier Khartoum had accepted the south's decision to become independent. In a statement read out on state television, Bashir said he remained committed to good relations between the north and the south.
"We respect the people of south Sudan's choice and we accept the result of the referendum according to what the commission announces," said the statement.
US President Barack Obama said Washington would recognise South Sudan as a free and sovereign state in July when the handover is official. European Union foreign policy chief Catherine Ashton promised that the EU would work with the new country, while US Secretary of State Hilary Clinton called on both the north and south to continue to work through the post referendum arrangements.