Luke Pearce, 19, was reported missing after a night out in Durham, sparking a week-long major search and rescue operation.
The first year engineering student from Hounslow, was last seen walking along the River Wear in the early hours.
The police were joined in their search by students from Durham University as they appealed for anyone with more information to come forward.
The inquest – which was attended by Luke’s mother Kate and three sisters – heard that before his disappearance, a group of police officers and some friends had both seen him.
But even though appearing drunk, they believed Luke was still capable of looking after himself.
Recording a verdict of accidental death, coroner Andrew Tweddle said there were no injuries to indicate he had been attacked and the cause of death had been drowning.
“He had been out on a night out, he had a good drink and it was a good night out,” said Mr Tweddle.
“He was seen by a group of police officers who said he was definitely drunk but not falling over drunk or incapable. Not at a level where they might have to intervene to keep him safe.
“He was seen by some of his friends and they did feel concerned about him. What happens next we will not know exactly, at some time he has gone into the river.
“We have an accident and that’s all it was, that sounds awful just to say that but that’s what it was. The accident has led to a fatal outcome.”
The inquest at Crook Civic Centre was told that around the area he is thought to have entered the water there is quite a short lawn and then it becomes reeds, which in the dark could be difficult to distinguish.
A week after he went missing in May, members of Durham Amateur Rowing Club contacted the police saying they had seen a body in the water near Baths Bridge.
More information: www.watersafetymap.co.uk/map/details/222
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