Meriam Yahia Ibrahim Ishag was condemned to death on May 15 under the Islamic sharia law that has been in place since 1983 and outlaws conversions under pain of death.
"The lady will be freed within days in line with legal procedure that will be taken by the judiciary and the ministry of justice," said Abdullah al-Azraq, a foreign ministry undersecretary.
Azraq, who spoke via telephone from London, did not elaborate.
The 27-year-old gave birth to a baby girl on Tuesday in a women's prison in Khartoum's twin city of Omdurman.
Ishag was born to a Muslim father but told the court during her trial that she had never been a Muslim herself.
The court gave her three days to "recant" her faith and when she refused, Ishag was handed the death penalty and sentenced to 100 lashes for "adultery".
Under Sudan's interpretation of sharia, a Muslim woman cannot marry a non-Muslim man, so any such relationship is regarded as adulterous.
Her case sparked international condemnation.
Britain and Canada had summoned the Sudanese envoys to their countries last week and told them the sentence violated Sudan's international human rights obligations.
United Nations experts have called the conviction "outrageous" and said it must be overturned.
An appeal was filed against the verdict but defence attorney Mohannad Mustapha said a hearing that was to have been held on Wednesday was postponed because the case file was incomplete.
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