Meriam Ibrahim's death penalty was overturned by an appeal court, the official Suna news agency reported.
She is married to a Christian man and was sentenced under Sharia law to hang for apostasy in May after refusing to renounce Christianity.
Her husband, Daniel Wani, said he was looking forward to seeing her.
He wanted his family to leave Sudan as soon possible, Mr Wani told BBC Focus on Africa.
This, hopefully, is the end of this story; a story of courage, faith and answered prayer. Bless you Meriam for not renouncing Christ. You are a hero!
The death sentence for Meriam Yahia Ibrahim Ishag, who gave birth to a daughter in prison not long after she was convicted, sparked international outrage.
"We are very very happy about this - and we're going to her now," Mrs Ibrahim's lawyer Elshareef Ali told BBC Focus on Africa.
"They have released her... she's on her way to home," he said.
Mr Ali said Mrs Ibrahim had shown "extraordinary courage" during her ordeal.
"It's a victory for freedom of religion in Sudan... By Mariam's strong position, we believe that in the future no-one will be subjected to such a trial," he said.
Analysis: James Copnall, former BBC Sudan correspondent
The outcry generated by Meriam Ibrahim's case was difficult for the authorities to ignore.
The government in Khartoum is already dealing with an economic crisis, and conflicts in Darfur, South Kordofan and Blue Nile. It simply does not need further ill-feeling - and it is worth pointing out that many of the most vocal opponents of the conviction were Sudanese, not foreigners.
In fact, Mrs Ibrahim's case looks like part of a recurring theme.
In 2009 Lubna Hussein, dubbed the "trouser woman", was arrested for wearing "indecent clothing" in public - in her case a pair of loose green trousers. She was at risk of a public flogging. Eventually she was given a small fine, which was then paid on her behalf to set her free. In 2012, Intisar Sharif Abdullah was sentenced to death by stoning for adultery, before she too was released without charge.
In every case, the authorities insist the justice system came to an independent decision, but many believe it bowed to public pressure.
|Daniel Wani with his daughter (left) and son (right)|
She has been in jail since February, along with her young son.
Mr Ali said he had not yet seen the appeal court's judgement, and had learned about the verdict through the media.
Sudan has a majority Muslim population. Islamic law has been in force there since the 1980s.
Even though Mrs Ibrahim was brought up as an Orthodox Christian, the authorities consider her to be a Muslim.
Her husband, who was born in South Sudan before it became independent from Sudan, went to the US in 1998 at the height of the civil war.
He met Mrs Ibrahim in 2011 on a visit to Sudan and they were married at the main church in Khartoum.