The body of a young man who went missing in Adelaide's River Torrens has been recovered from the water after a search involving police divers.

Police said the 19-year-old from Smithfield was reported missing about 4:50pm after he was seen in the water but did not resurface.

That prompted a major search operation involving more than a dozen police officers near the University of Adelaide, west of the university footbridge.

Police said the man's body was recovered about 7:10pm.

The death is being treated as an accidental drowning and police said a report would be prepared for the coroner.

Police are appealing for information from anyone who may have seen the man go into the water.