Heather Still, 13, was struck at Whitecraigs station in East Renfrewshire at around 2pm yesterday.
She died at the scene.
In a statement released through British Transport Police (BTP) her family said: "We are completely devastated at the senseless loss of our beautiful and much loved daughter and sister, Heather, and words cannot express our pain and despair.
"We would also like to thank everyone for their kind messages and support that we have received and also request that our privacy be respected at this incredibly difficult time."
Heather was a pupil at Mearns Castle High School in Newton Mearns, East Renfrewshire.
Headteacher Dean Smith said: "We are deeply saddened by the tragic news of the loss of a bright and popular pupil, Heather Still.
"This is a time of profound sadness for our school community and we are concentrating on providing support to our pupils and staff who are understandably shocked and upset.
"We ask for privacy for the family and for the school to allow us to make sense of this loss. Our thoughts are with Heather's family."
BTP said there are no suspicious circumstances surrounding her death and a report has been sent to the Procurator Fiscal.
The train was the 2pm Neilston to Glasgow Central service.