The mother-of-five left a detention facility in southern Punjab before being flown to Islamabad amid tight security, Associated Press said.
According to Reuters, she has been taken to a "secure location" in the capital owing to continued fears over her safety.
The news agency quoted the information minister Fawad Chaudhry as saying Ms Bibi remained in Pakistan on Thursday.
A petition demanding a review of the decision by Supreme Court judges to acquit her may frustrate plans for Asia Bibi to flee the country.
Chowdhry from the British Pakistan Christian Association told Premier: "It is a moment of great joy and we praise God for making the impossible possible.
Only through his divine intervention have we seen this wonderful result today."
Ashiq Masih (pictured above, centre) - the husband of Asia Bibi - had urged the UK, US and Canada to grant asylum to his wife. Spain and Italy have each offered her sanctuary.
The ruling prompted thousands of people to join protests in several major cities, demanding that she be publicly executed.
Asia Bibi spent eight years on death row after being convicted of blasphemy. She had been accused of insulting Islam's prophet Muhammad. Ms Bibi always denied any wrongdoing.
The Supreme Court in Pakistan is not known to review its rulings. But such a process could take years.
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