Southern Sudan voted overwhelmingly for independence, election officials have confirmed.
They said nearly 99% of the voters in January's referendum were in favour of dividing Africa's biggest country.
Earlier, Sudanese President Omar al-Bashir again said he would accept the outcome of the vote.
The poll was agreed as part of a 2005 peace agreement ending more than two decades of civil war between the south and north Sudan.
Although the vote was peaceful, tension remains high in parts of the oil-rich border region.
At least 50 people were killed over the weekend in fighting between soldiers in south Sudan's Upper Nile state.
On Monday, the Southern Sudan Referendum Commission announced in Khartoum that 98.83% of the voters had backed independence.
"Those who voted for unity were 44,888, that is, 1.17%. Those who voted for separation were 3,792,518, that is, 98.83%," commission head Mohamed Ibrahim Khalil said.
The BBC's Peter Martell in the southern capital Juba, says some people have spent most of the day getting ready to celebrate the announcement.
"Now I am a first class citizen in my own country," housewife Abiong Nyok told the BBC.
One woman - a northerner - cried after the announcement, saying she had relatives in the south, the BBC's James Copnall in Khartoum says.
Earlier on Monday, President Bashir reiterated that he would accept the outcome of the vote, allaying fears that the split could re-ignite conflict over the control of the south's oil reserves.
"We accept and welcome these results because they represent the will of the southern people," Mr Bashir said on state TV.
James Copnall says the president has made similar comments before, but this firm and public commitment will reassure any southerners still wondering whether Khartoum would go back on its word.
The president said he was committed to good relations with the future Southern state. The US has said it will remove Sudan from a list of countries it accuses of sponsoring terrorism if the referendum goes well.
South Sudan's leader Salva Kiir pledged co-operation with Khartoum in the future, saying there were "many things that connect the north and the south".
"The (freedom) of the south is not the end of the road, because we cannot be enemies. We must build strong relations," said Mr Kiir, who is also Sudan's Vice-President.
In Washington, President Barack Obama congratulated the people of Southern Sudan for "a successful and inspiring" referendum, saying the US intended to formally recognise Southern Sudan in July.
British Prime Minister David Cameron welcomed the announcement of the poll's result, saying both "North and South now need to work together to implement the remaining provisions" of the 2005 peace deal.
A European Union representative in Sudan said the bloc "looks forward to further developing a close and long- term partnership with Southern Sudan".
UN Secretary General Ban Ki-moon urged the international community "to assist all Sudanese towards greater stability and development" and offered the UN's help to both sides, the AFP news agency reports.
In the last half century southerners have fought two devastating civil wars with Khartoum, in which more than two million people are estimated to have died.
The south sees itself as different in cultural, religious and ethnic terms from the north, and believes it has suffered years of discrimination.
The BBC's James Copnall says the announcement of the final results will not be the end of the process.
Issues including the disputed border region of Abyei, citizenship, legal matters and resources like oil will need to be negotiated.
Though it is rich in oil, Southern Sudan is one of the least-developed regions on earth, and ethnic tensions and troubled relations with the north will provide constant security challenges.
Our reporter says that many southerners feel what they consider a forced union with the rest of Sudan has been a catastrophe.
He says that although when Southern Sudan becomes independent in July it will face huge problems, the dominant emotion for southerners once the results are announced will surely be one of huge joy.
The formal declaration of independence will be made on 9 July 2011 - six years after the peace deal, which led to the referendum, took effect.