Mr McFaul is not expected to arrive back in Northern Ireland before the weekend.
The 36-year-old, originally from Andersonstown and has dual nationality, was part of a large group of foreign oil workers kidnapped at the BP gas field in the North African country.
The terrorist attack was led by Islamist militants in the early hours of Wednesday morning.
The married father dramatically escaped the following day amid intense fighting between the kidnappers and Algerian troops.
He told his family he was in one of five jeeps containing hostages and captors, which were on the move when Algerian Special Forces launched a military operation.
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 also emerged that Semtex explosives had been strapped around his neck.
On Friday a spokesman for the family said he was mentally and physically exhausted after the ordeal but that his mood was bright.
The spokesman said the Belfast man was on a London-bound flight specially chartered by his employer.
He is due to meet officials from the Foreign Office for a full debrief before returning to Belfast, amid UK-wide travel disruption caused by heavy snowfall.
It appears to have been a large, well co-ordinated and heavily armed assault and it is probable that it had been pre-planned.
In the House of Commons on Friday morning, Prime Minister David Cameron confirmed the government's priority was "the safety of British nationals involved, the repatriation of those killed, and the evacuation of the wounded and freed hostages."
Several British workers remain at risk, he said - but the precise number of hostages and the extent of casualties still remained unclear on Friday.
Mr Cameron confirmed that British officials were not told ahead of time about the military intervention planned by the Algerian Government.
He made it clear that he would have preferred to be informed ahead of proceedings, but the Algerians had to act "immediately" due to the threat posed to the hostages' lives.
He said hostages from eight countries had been kidnapped - including an unknown number of Algerians.
The attack started when two buses en route to the In Amenas airfield were attacked by Islamist terrorists killing two people - one of whom was British - before further attacks on the residential compound and the gas facility, the Prime Minister told MPs.
The dead Briton's family were informed on Wednesday, he added.
Situated close to the border with Libya, the gas field is in the middle of the Sahara desert and is one of the most remote locations in the world.
An Islamic group claimed the operation was in retaliation for the French military intervention against al Qaida rebels in neighbouring Mali.
On Thursday, Mr McFaul's mother Marie told UTV they were simply "thrilled to bits" to find out he had survived the terrorist attack.
"I'm sorry for the other people that are still there, but we're very happy - over the moon," she said.
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".