A total of 98.83 percent of voters from Sudan's oil-producing south chose to secede from the north in last month's referendum, according to a video display of the vote seen by Reuters at the venue of the announcement.
The referendum is the climax of a 2005 north-south peace accord that set out to end Africa's longest civil war.
Sudan's President Omar Bashir earlier said he accepted the result of the vote, allaying fears that the split could reignite conflict over the control of the south's oil reserves.
"Today we received these results and we accept and welcome these results because they represent the will of the southern people," Bashir said in an address on state TV.
Southern officials say the question of a name for the new state is unresolved but it could become just "South Sudan".
South Sudan's leader Salva Kiir added to the conciliatory mood by promising he would help Khartoum campaign for the forgiveness of the country's crippling debts and the easing of international trade sanctions in coming months.
Both sides did avoid major outbreaks of violence over the past five years. But they failed to overcome decades of deep mutual distrust to persuade southerners to embrace unity.
Hundreds of people started gathering in the southern capital Juba on Monday to celebrate the results. "Today I don't fear war anymore, it is the past ... Our leaders have made friends with the north, but for me, I can never forgive them for what I have seen. I don't hate them now, but I never want to see them again," said Riak Maker, 29, as men drummed and women ululated around him.
Washington has signaled it is ready to remove Sudan from its list of state sponsors of terrorism after a successful referendum, and help in easing crippling trade sanctions.
Deep uncertainties remain over the economic and political stability of both territories over the next five months of intense negotiations over how to share their oil revenues and other unresolved issues.
