In a letter sent to parents, staff at the north Leeds secondary campus named the tragic student as Thomas Coupe, who was in his final year at the school.
He was helping out at a post-16 open day event for prospective sixth formers on Saturday morning when he collapsed.
Teachers gave first aid to the popular year 13 pupil, who was then taken to St James's Hospital, but he never regained consciousness.
The teenager had been speaking to pupils about studying A Level politics before he died.
Thomas, known as Tom, attended Kerr Mackie Primary School on nearby Gledhow Lane before starting at Roundhay. His sister Lucy is also thought to have been a pupil at the school.
One parent described how visitors were asked to leave the sixth form pavilion building just before midday due to a medical emergency.
A letter sent out to families of children at the school read:
"We write with some very sad news that we would ask you to share with your child. Thomas Coupe (year 13) died in hospital yesterday evening after collapsing during the school’s Open Day event.
"Despite the very best efforts of several of our staff and a team of paramedics both at school and then St. James’s Hospital, Tom never regained consciousness.
"Tom was a bright, caring and responsible young man demonstrated by the fact that yesterday he was supporting the Politics department in his own time to promote the subject to potential new sixth formers. We will miss him.
"The school will be open as normal for Y7-Y12 students on Monday. If your daughter or son finds this news particularly difficult, we would ask you to please contact us at school
tomorrow and we will put the appropriate support and care in place. We will have a team of people available to offer support, should your child need it.
I am sure you will join us in sending our deepest sympathies to Mr and Mrs Coupe, Lucy and their wider family and friends at this awful time."
Roundhay School headteacher Matthew Partington added:
"It is with immense sadness that I can confirm that one of our students passed away unexpectedly at the weekend. Our thoughts are with his family and friends at this sad and difficult time.
“Our whole school community has been shocked and deeply saddened by the loss of one of our own, and we are making support available for students and staff as needed.”
A tribute on Twitter read:
"Such sad news. A great character in and out of the classroom. Staff dealt with the situation with the utmost professionalism. RIP Tom."