A Sudanese foreign ministry official said Meriam Ibrahim, who gave birth to a daughter in her prison cell last week, will be freed in a few days.
Ms Ibrahim was brought up as a Christian but a judge ruled she should be regarded as Muslim because that had been her father's faith.
The 27-year-old refused to renounce Christianity and was sentenced to death by hanging.
The court also annulled her marriage, then sentenced Ms Ibrahim to 100 lashes for adultery.
However, an official at Sudan's foreign ministry said the country guarantees religious freedom and is committed to protecting Ms Ibrahim.
Khartoum had been facing international condemnation over the death sentence; British Prime Minister David Cameron described it as "barbaric".