Blake Ross, who was in care, was reported missing from Howdenhall at 15:15 on Saturday.
After being found unwell 48 hours later on the number four bus at Leopold Place he was taken to the Royal Hospital for Sick Children where he died.
An investigation is now being carried out into the actions the police took in relation to the case.
It has been confirmed that the Crown Office and Procurator Fiscal had instructed the Police Investigations and Review Commissioner (PIRC) to conduct an independent investigation.
Edinburgh Council will also conduct a multi-agency significant case review into Blake's death.
When a child in care dies, such reviews are standard practice.
Lothian Buses said the driver of the bus radioed his control room to report that Blake was unwell.
A supervisor attended and police were also called before the teenager, who was thought to be one of triplet brothers, was taken to hospital.
The youngster's death, which is understood to have been related to his diabetes, is currently being treated as unexplained and police inquiries are continuing.
Blake had recently featured in a short film produced by Edinburgh Leisure about children in care.
Tommy George, community development manager at Edinburgh Leisure said: "It [the film] showed how physical activity and sports impacts positively on the lives of young people in care.
"Everyone who came into contact with Blake is deeply saddened to hear this news and we send our condolences."
Supt Lesley Clark, of Police Scotland, said: "The matter has now been referred to the Police Investigations and Review Commissioner.
"As in all matters concerning police contact before death, we will provide any necessary assistance to the PIRC as they conduct their investigation and we await the outcome of their report.
"This is a tragic set of circumstances and thoughts and condolences are with Blake's family and friends."
A City of Edinburgh Council spokesperson said: "We are deeply shocked at Blake's sudden death and our thoughts are with his family.
"We will continue to liaise closely with Police Scotland as they carry out their inquiries."
A 13-year-old boy who fell ill after going missing in Edinburgh without his diabetes medication has died.