Elizabeth and Maged El-Nakla, from Dundee, were among close to 100 British nationals allowed to pass through the Rafah border crossing into Egypt.
The first minister said on Friday: “We're hugely relieved that Nadia’s parents have been able to leave Gaza. We thank everyone for their messages of comfort over the past few weeks.
“Our thoughts are very much with those who cannot leave and [are] still suffering in Gaza. We will continue to raise our voices for peace.”
At least 92 British citizens, as well as 35 dependents were allowed to cross Rafah on Friday according to a list shared with The Independent.
Also among the list of names were British citizens who have spoken to The Independent about trying the border multiple times in the past. Their family members who were not on today’s list said they had left for the border to try again.
Sources on the Egyptian side of the border said in the late morning at least two buses with around 100 people were entering Egypt.
When Mr Yousaf phoned his 14-year-old stepdaughter during a break at school on Friday, the pair both shared “a few tears” in relief at the news. The first minister said: “That was a really special moment, being able to phone my eldest.
“We both shed a few tears and she’s just elated and really happy. She has been exceptionally worried.
“My four-year-old [Amal] we can protect her to an extent but my 14-year-old, Maya, knows everything, watches everything and it has been hugely distressing for her.”
The situation has taken its toll on Mr Yousaf and his family, but he thanked those who sent messages of support from across the political spectrum and around the world.
Mr Yousaf added: “I wouldn’t be lying by saying the last four weeks have been, if not the most difficult four weeks of our lives, certainly amongst the most difficult four weeks of our lives.
“Every night we’ve gone to bed not sleeping because we’re worried about whether or not my mother and father-in-law are going to make it through the night.
“There were moments we thought that was it. We were just bereft really at the grief, thinking they had been killed.
“These last four weeks have been a living nightmare for our family, we are so thankful for all of the messages of comfort and prayers that we have received from across the world, and indeed from across the political spectrum in Scotland and the UK.”
Mr Yousaf’s in-laws travelled to Gaza to visit family prior to the conflict erupting and became trapped,
Mr and Ms El-Nakla had spent the past two weeks in a house where dozens of people were sheltering.
They had travelled to the border on three previous occasions without success. Speaking to BBC News from a coach bound for Cairo, Ms El-Nakla said: “We are completely exhausted as we haven’t slept properly for the past 27 days.
“The past few days have been particularly traumatic. We don’t really know what’s been going on in the outside world as there’s been no internet, electricity, clean water and food has been difficult to get.”
The Rafah crossing, which offers the only way in and out of Gaza, was opened by Egypt on Wednesday.
A list published overnight into Friday by the Palestinian Border Authority said those named must be “present at 7am in the outdoor halls of the crossing to facilitate their travel”.
According to Palestinian officials, 355 foreign passport holders and their dependents crossed the border on Friday.
The Foreign Office has said UK nationals were able to make it into Egypt, but have declined to say exactly how many.
Security minister Tom Tugendhat told Sky News earlier in the day: “Different families will have different pressures and different ways, so you will understand that it is not very easy to give a running commentary and it would be the wrong thing to do.
“I can give this absolute assurance that the UK government from the prime minister, the foreign secretary, me and many others, have been absolutely committed to making sure we look after British citizens as best as we possibly can and we help to get them out of this incredibly dangerous situation.”
Routes in and out of the region were closed after Hamas – which is proscribed as a terrorist group in the UK – attacked inside Israel on 7 October, killing more than 1,400 people and taking at more than 240 people hostage.
In respoonse, Israel has been carryiong out an extensive bombing campaign on Gaza, as well as ground operations. More than 9,000 people have been killed in the Gaza Strip according to the health ministry there.
Aid agencies are battling a humanitarian crisis in the war-ravaged territory with limited resources, amid calls for the international community to increase its efforts.
It is understood that James Cleverly, the foreign secretary, spoke to Ayman Safadi, minister of foreign affairs in Jordan, and UAE foreign minister Abdullah bin Zayed Al Nahyan on Thursday about the humanitarian situation in Gaza.
He also spoke to Israel’s minister of strategic affairs, Ron Dermer, about ensuring British nationals are able to cross safely as soon as possible into Egypt, while reiterating the UK’s solidarity with Israel and its commitment to finding a two-state solution.