The 15-year-old has been named locally as Sephora Laforge. She was a pupil at George Watson's College.
Police cordoned off the park, on the edge of the New Town, on Tuesday morning after the discovery of a body at around 7.40am.
The death is not being treated as suspicious.
Friends of the girl described her as 'one in a million'.
One posted: "'I wish I could tell her everything is going to be OK. We are all devastated."
Another friend added: "Gone but never forgotten, gorgeous”.
It is understood they are organising a lantern tribute to the teenager in the park over the coming week.
A spokesperson for Police Scotland said: "Inquiries into the circumstances surrounding the death are ongoing and the death is being treated as unexplained at this stage.
“A report will be submitted to the Procurator Fiscal.”