Olivia Raby, 14, died after collapsing at St Ambrose Barlow High School in Swinton on Thursday, May 22. It is thought she may have had a heart attack.
The youngster was a keen athlete and played netball and hockey as well as rounders.
Olivia’s heartbroken parents, Tracey Raby and Mark Barton, said: "We loved Olivia very much and we can’t begin to put it into words how we feel.
"Olivia was a happy and beautiful young daughter with her whole life ahead of her and she will be deeply missed by everyone who knew her.
"Olivia gave us 14 wonderful years and no-one can take away the precious memories of our time together.
"Olivia was not only our daughter but our best friend and she will be forever in our thoughts."
Her tragic death has triggered a huge number of tributes from family, friends, and schoolmates, who have posted messages on websites and left flowers at a tree in the grounds of the school.
A post mortem examination is due to be carried out later this week.
Olivia collapsed while playing rounders in a lesson at the school in Shaftesbury Road.
An ambulance operator gave resuscitation instructions to a member of staff over the phone.
Paramedics continued to try to save her at the school and on route to hospital.
Schoolfriend Jessica Johnston described Olivia, who lived in Coronation Street, Swinton, as a ‘really nice person’.
Jessica, 15, said: "She was in the year below me at school but I know she was a really nice person.
"Everyone really liked her and the whole school was in shock by what happened."
Headteacher of St Ambrose Marie Garside said: "The whole of the school community has been totally shocked and stunned by these very tragic events.
"Olivia was a very gifted member of our school community, not just in terms of her academic and athletic ability but in her generosity of spirit and kindness.
"Our heartfelt sympathy and prayers are with the family and our priority is to provide all the support that we can both to them and to the larger school community."