On Monday, a hold-up over paperwork foiled plans to fly the Ukrainian youngsters from Warsaw to London.
However, a Virgin plane has landed in Warsaw and is expected to return to London later. The group will then go directly to their temporary home in Callander, Stirlingshire..
The charity Dnipro Kids, which was set up by Hibs FC fans, enabled many of the children to flee Ukraine for Poland. A second group was accompanied by Sally Becker, founder of Save a Child.
The Edinburgh-based charity has made arrangements for the children, who range from infants to older teenagers, and their seven legal guardians to stay in a hostel in Stirling before being moving them to Edinburgh. The children will be in family-style groups similar and will not leave Scotland until it is safe for them to return.
Hibs supporter and SNP MP Ian Blackford, the party’s Westminster leader, supported moves for the children to seek sanctuary in Scotland.
Speaking in the House of Commons, he thanked the Scottish and UK governments for helping make arrangements.
Mr Blackford said: "This is a good day for these 50 young people but let's hope it's the beginning of something much more significant for more young people that we can offer sanctuary to.”
On Monday the Home Office said delays took place due to problems authorising the backgrounds of the children, who do not have family members to act on their behalf.
Mr Blackford said it had taken time to get the paperwork in order for the children to be evacuated to Scotland because they had to address all safeguarding concerns before they could be moved to another country.
Writing on Twitter, he said: "This wasn't just about visas but the due diligence of a sovereign state getting the necessary permissions to allow the children to travel. We would all want the same for our children."
He added that the children and their carers would be given privacy on the journey to the UK and the "time and peace to settle into new surroundings".
Dnipro Kids chairman Steven Carr, who led the evacuation effort from Lviv in Ukraine and Poland, had promised the children they would be made welcome in Scotland.