Blake Ross, 13, was discovered unwell on a Lothian bus on Monday afternoon, two days after police launched a major search operation after he disappeared from Howdenhall in the south of the city.
The Police Investigations and Review Commissioner (Pirc) is now investigating officers’ actions in relation to the incident.
The teenager, who lived at the city’s St Katharine’s care unit, is understood to have suffered from diabetes and did not have access to his medication while he was missing.
Police Scotland confirmed Blake had been taken to the Sick Kids Hospital on Monday, where he died at around 9pm.
His death is currently being treated as unexplained and inquiries are continuing.
A passenger who was travelling on a number 4 Lothian bus around 2pm on Monday told how Blake got on the bus with his hood up, and said he “slid down the bus stop” on Leopold Place after getting off the service.
She said: “I didn’t notice him getting on at first but after the ticket inspector appeared there was a small commotion happening at the front of the bus.
“I heard the boy, who was sitting with his hood up at first, tell the ticket inspector a few things including that he needed a hot drink. I think the ticket inspector knew it was Blake – the boy that was missing – as he kept communicating with the driver.
“The inspector asked him if he was feeling OK because he kept falling asleep.
“He really didn’t look well. Then when he got off the bus he stumbled and slid down the bus shelter.”
Superintendent Lesley Clark, of Police Scotland’s Edinburgh Division, said: “This is a tragic death of a young boy and our thoughts are with Blake’s family at this very difficult time.
“In the coming days and weeks we will be working with our relevant partners to support his loved ones.”