Detectives leading the case believe the body is that of teenager Jasmine Macquaker, who vanished on Sunday.
Although formal identification has not yet taken place, the parents of the 14-year-old have been informed of the sad discovery.
The death is being treated as unexplained with officers hoping a post-mortem examination will shed light on her final moments.
Jasmine, whose father is understood to be an Edinburgh investment manager, is a former pupil of Cargilfield, Scotland’s oldest independent boarding and day prep school.
She was said to be an exceptionally talented student who won prestigious art and writing competitions, including the National Schools’ Handwriting Competition in 2014.
School magazine the Cargilfield Publiciser revealed in Spring 2014 that the teenager was awarded a scholarship to study art at Queen Margaret’s, a prestigious independent girls’ boarding school in York.
It is understood she was also a keen swimmer who was a member of Inverleith Swimming Club in the Capital. She also competed in a number of sporting events in York, including a biathlon and pentathlon.
Friend Charlotte Hickie paid a poignant tribute on Facebook yesterday, saying: “I love you Jaz and I miss you lots. You were the nicest and kindest friend anyone could ever have and you will be seriously missed.”
Police Scotland issued an urgent appeal for information on Jasmine’s whereabouts just after 5am yesterday, after receiving reports of her out of character disappearance.
The teenager, from Edinburgh, was last seen at Dalmeny railway station near South Queensferry, at around 8.30pm on Sunday.
It is thought she had travelled to Dalmeny from Edinburgh Waverley at around 8.15pm. Officers launched an extensive search. However, it was a member of the public who found a body on the shore at North Queensferry, Fife, at around 7am yesterday.
Forensics experts erected a tent at the scene before the body was taken away.
A police spokesman said the death was being treated as “unexplained” and added: “A formal identification is yet to be carried out. However, Jasmine’s family have been informed and have requested that their privacy be respected at this very difficult time.”