The body of the teenager was found on the prominent city centre hill early on Saturday morning, only a few hours after she had been initially reported missing.
Calton Hill was cordoned off by police for several hours after the discovery.
Her death is currently being treated as “unexplained” ahead of full post mortem tests, with inquiries ongoing.
The girl, who has now been named as Mhari O’Neill from Willowbrae, was a popular fifth year pupil at Portobello High School.
Headteacher Ruth Mackay led a special assembly at the school yesterday and pupils were offered support through the day.
In a statement issued today, Ruth McKay said: “Everyone at the school is deeply saddened and shocked to hear about Mhari’s sudden death. The Portobello school community is a very close one and our thoughts are with her family.
“Mhari was a lovely, friendly girl who was well-liked by both staff and young people. Her bubbly, out-going nature and ready smile will be much-missed in school.
“We have been ensuring that young people and staff are offered all the support they need at this sad time.”
A spokesperson for the City of Edinburgh Council said: “Everyone at the school has been extremely shocked to hear about the sudden death at the weekend. We have been ensuring that young people and staff are offered all the support they need.”
In a statement issued through Police Scotland, the family of Mhari O’Neill said: “Mhari was much loved by all that knew her and we know that her passing will have a profound impact on her closest friends, as it has ourselves.
“Mhari was considering applying to attend university and one of her main passions was music; she loved going to gigs.
“What we need now is to find out exactly what happened to Mhari and we want anyone who thinks they may have information to get in touch with the police.
“We thank everyone for their support and ask that we be left in privacy to grieve at this time.”
Police said they believe Mhari had been in the city centre with a friend before making her way to Calton Hill on Friday, just hours before her tragic death.
Detective Inspector Susan Balfour from the Major Investigation Team said: “Our deepest sympathies are with Mhari’s family and friends at this time and we are carrying out a thorough investigation to establish the full circumstances surrounding her death.
“We believe Mhari met a friend in the city centre, near to Waverley Station, on Friday afternoon before making her way to Calton Hill sometime later. However, we are keen to hear from anyone who believes they may have seen her throughout the evening or early morning of Saturday, so we have a clearer picture of all her movements.
“Mhari’s death is currently unexplained and her movements for a number of hours prior to her body being found are unaccounted for.
“We are committed to providing Mhari’s family with as much information in relation to her death as possible and anyone who can assist with our ongoing inquiry is urged to come forward.
“Naturally, we are working closely with partners in Education to help support any young people who may have been affected by Mhari’s death.”