Wrexham County Council has conceded to allow the 16-year-old foster child to attend the prestigious Scottish school after an anonymous benefactor stepped forward to pay the fees.
She had already passed the entrance exam for Gordonstoun with flying colours and had been offered a place.
On Wednesday, Suzanne put her case to Wrexham council, which said it would consider her plight.
On Friday, the council's Director of Personal Services, Malcolm Russell, said: "We recognise Suzanne's views and that her grandparents and Gordonstoun are very keen for her to attend that school and have indicated that they will support her and assist financially."
The local authority had refused to help with the £19,000-a-year fees and so far the council has not revealed details of any payments towards Suzanne's fees.
But Mr Russell said: "We have agreed to respond to the views expressed by agreeing to her placement at Gordonstoun provided that a number of appropriate safeguards can be put in place.
"As Suzanne is still a young person who is looked after by Wrexham County Borough Council we ask that she is now given space to continue with her life."
Life savings
The Children's Commissioner for Wale, Peter Clarke, said he was "delighted" by the decision and commended the council for changing its mind.
"It is very important that children looked after in care are encouraged to have high educational aspirations and to be supported in achieving their goals," he said.
"I would like to congratulate Suzanne herself for the way in which she has campaigned tobe given the chance to realise her chosen path."
Her grandparents, Ida and John Turley - both retired teachers - had offered their life savings of £20,000 to help fund the two-year course.
But the offer of £19,000 to pay the Gordonstoun fees in full means they can keep their money.
Suzanne had also threatened to take Wrexham Council to court, if they did not allow her to go to the flagship school.
She had even enlisted the help of the Commisioner and her local Welsh Assembly member to try to overturn the decision.
The teenager said that she was intent on pursuing a theatrical career and dreams of running her own theatre.