Kamau McCallum-James, 18, was reported missing by his mother from their home in Huddersfield just before midnight on August 21.
Police divers had been scouring the River Calder, off Leeds Road, near Cooper Bridge Road, in the search for the youth, who was described as vulnerable.
A helicopter was also used, as well as CCTV and police dogs.
It emerged the “quiet and polite” youngster had only recently gained a place at Teesside University in Middlesbrough.
West Yorkshire Police has confirmed the body found at Cooper Bridge was Kamua.
In a statement they said: "Police can confirm that the body which was discovered on Friday afternoon (30 August) is missing teenager Kamau McCallum-James.
"There are not believed to be any suspicious circumstances and a file has been prepared for the coroner for an inquest.
"Kamau’s family have been updated and are being supported by Kirklees District Police. They have requested privacy at this very difficult time."