"It was a peaceful process. It was a transparent process," panel Chairman Muhammad Ibrahim Khali said at a ceremony in Khartoum reported by CNN.
The expected landslide result set off jubilation in Juba, the southern capital.
"The results of the referendum mean I am free today," housewife Abiong Nyok told the BBC. "Now I am a first-class citizen in my own country."
In Khartoum, Sudanese President Omar al-Bashir issued a decree accepting the result, Xinhua reported, citing state TV.
U.S. President Barack Obama congratulated "the people of southern Sudan for a successful and inspiring referendum."
Secretary of State Hillary Clinton said Washington is "initiating the process of withdrawing Sudan's state sponsor of terrorism designation."
South Sudanese leader Salva Kiir promised to help the north press for debt cancellation and the easing of trade sanctions.
The formal declaration of independence is scheduled July 9. The two sides still must deal with many issues, including currency, citizenship, national debt, the division of oil reserves and the disputed border region of Abyei.
Human rights groups are alarmed at suggestions that Bashir, indicted for war crimes in Darfur, should be rewarded for accepting the vote, The Guardian reported.
"Only this week the Darfur genocide continues as President Bashir's troops have swept into camps and villages with armored attacks and aerial bombardment of unarmed civilians. Coming after the height of the world's attention on the referendum, al-Bashir must face closer scrutiny on Darfur and his continued human rights abuses or more horrors are inevitable," said Olivia Warham, director of Waging Peace.
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