The 36-year-old told his family he was in one of five jeeps containing hostages and islamist kidnappers, which were on the move when Algerian special forces launched a military operation on Thursday.
It is understood four of the vehicles in the convoy were bombed while the fifth - which was carrying Mr McFaul - crashed.
He managed to escape from it and made it to a safe camp.
It has also emerged that Semtex explosives had been strapped around Mr McFaul's neck.
The family exclusively revealed the news of his release to UTV's Sharon O'Neill.
Stephen's mum Marie said they were simply "thrilled to bits" to find out he was free.
"I'm sorry for the other people that are still there, but we're very happy - over the moon," she said.
"He'll not be back. He'll take a job here in Belfast like the rest of us."
His tearful son Dylan added that he couldn't wait for his dad to now return home.
"I'll never let him go back there," the 13-year-old said, adding that as soon as he sees him he'll just "give him a big hug and never let go".
It's been a tough 48 hours - but we've come through it ...
Christopher McFaul, Stephen's dad
The Irish Department of Foreign Affairs and Trade later released a statement confirming that the man, who is originally from Andersonstown and has dual nationality, was safe and well and no longer a hostage.
A short statement from the First and deputy First Ministers on Thursday evening also welcomed Mr McFaul's release.
Peter Robinson and Martin McGuinness said they hope that he can return to his family in the near future and added that their thoughts are with the other oil and gas workers being held.
Tánaiste Eamon Gilmore said he was "extremely thankful and relieved" by the news.
"This is the news that we all wanted to hear," he said.
"At the same time, my thoughts are with the other workers who are caught up in this terrible situation, and with their families who are also waiting for news at this difficult time.
"We continue to liaise with the Algerian authorities and with the authorities of the other countries affected by this incident."
The latest developments come after reports that some of the 41 foreign hostages and their captors had been killed in a helicopter strike by the Algerian military, aimed at ending the siege.
The number of dead remained unclear on Thursday night.
The hostage crisis began on Wednesday morning, when the armed gang seized the gas field.
Two people were killed in the initial attack, which the Islamic group claims was in retaliation for the French military intervention against al Qaida rebels in nearby Mali.
Prime Minister David Cameron, who has postponed travelling to the Netherlands to give a speech on Europe, has warned that the UK should be "prepared for the possibility of further bad news".
One British citizen is known to have died in the crisis and several others remain caught up in it.
"It's a fluid situation - it's ongoing, it's very uncertain," Mr Cameron said.
The gas field is a joint venture by BP, Norwegian firm Statoil and Algerian state oil company Sonatrach.
The Algerian interior ministry said the attack began when three vehicles carrying heavily armed militants ambushed a bus carrying employees from the gas plant to the nearby airport.
Initially they were driven off, but the gang then headed for the main complex - where they took a number of workers hostage.
We should be prepared for the possibility of further bad news, very difficult news, in this extremely difficult situation.
PM David Cameron
The Irish and British governments have been working alongside other countries in liaising with the Algerian authorities.
Taoiseach Enda Kenny said he was relieved by the release of Stephen McFaul, but that his thoughts remained with all others caught up in the traumatic situation.
"I am greatly relieved to hear that Stephen is safe and well," he said.
"I believe he has already spoken to his family in Belfast and I wish him a safe return home to his loved ones.
"I would like to pay tribute to all those who have been involved in the effort to resolve this crisis and my thoughts are with the other oil-field workers and their families."
Mr Cameron held a number of emergency cabinet meetings, known as COBRA, on Wednesday and Thursday.
It has emerged that British officials were not told ahead of time about the military intervention planned by the Algerian government.
The Prime Minister made it clear that he would have preferred to be informed in advance, but the Algerians said that they had to act "immediately".
Mr Cameron remains extremely concerned and says that the situation in Algeria is "very serious and difficult".
He spoke to both US president Barack Obama and French President François Hollande on Thursday.
Bob Dudley, BP Group Chief Executive, said they want to ensure their staff are safe and to support their families during this "anguishing" time.
"All our efforts are focused on supporting the authorities to secure a peaceful resolution of the situation and the safe return of our colleagues, and all other workers being detained," he said.
He said reports of casualties, or any release or escape of hostages, were unable to be verified by the company due to a lack of "confirmed or reliable information".
As a precautionary measure, staged plans are underway by BP to bring a group of non-essential workers out of the North African country.
Meanwhile earlier claims that a second Northern Irish hostage was being held captive have turned out to be unfounded.