Eilidh MacLeod, 14, from Barra in the Outer Hebrides, had been missing since the explosion at the Ariana Grande concert on Monday night.
Her friend, Laura MacIntyre, 15, was seriously injured and is being treated in a Manchester hospital.
Greater Manchester Police confirmed on Wednesday that all of the victims had been accounted for.
Eilidh's parents have issued a statement via the police.
It said: "Our family is devastated and words cannot express how we feel at losing our darling Eilidh.
"Eilidh was vivacious and full of fun. She loved all music whether it was listening to Ariana or playing the bagpipes with her pipe band.
"As a family we would like to express our thanks and gratitude for the support and kind messages we have received at this difficult time."
Earlier, families in the Outer Hebrides island had made desperate appeals when the girls failed to get in touch after the blast which killed 22 people and injured at least 59 others.
Eilidh and Laura were pupils at Castlebay Community School and their headteacher said the incident has left everyone in shock.
Annag Maclean said: "The recent incident in Manchester was a planned and violent act targeted at young people enjoying a social event.
"Our school and island community are in shock, feeling numb and struggling to come to terms with it.
"Our thoughts and prayers are with Eilidh and Laura, their family and friends as they struggle to cope.
"As headteacher, I am confident that our school and our community will continue to support Eilidh and Laura's families.
"I have worked with my colleagues in the authority and other agencies to ensure that all necessary support is available to staff and pupils."
On Wednesday, Catholic Bishop of Argyll and the Isles Brian McGee travelled to the island to visit the girls' families.
He said: "This is a time of terrible anguish for the MacLeod and MacIntyre families.
"Spending time with the relatives of both girls was a reminder of the human cost of acts of terror.
"Such acts leave families broken, lives scarred and innocence destroyed. My thoughts and prayers are with the families at this traumatic time."
First Minister Nicola Sturgeon told MSPs that Police Scotland family liaison officers were providing support to the teenagers' families.
Church of Scotland minister Rev Dr Lindsay Schluter said no-one on the island had been unaffected by the terror attack.
"People have been numbed by what has happened to the two girls and everybody continues to be very anxious about their welfare," the minister for Barra and South Uist said.