Callum Dawson, who was just 17, went into the water with friends near to the Cardigan Fields retail park in Kirkstall, on the early evening of June 26 last year.
His body was found by a police underwater rescue team in the early hours of the following morning.
The inquest into his death was held at Wakefield Coroner's Court this week.
Originally from Bradford, Callum was a joinery student who had been living at a hostel on Dewsbury Road in Beeston.
The hearing was told that his two friends went into the water first and began swimming towards the other side, followed by Callum. One described the water as being very cold.
A third friend, who remained on the bank, said he then saw Callum beginning to struggle as he reached half way across the river.
In a statement read to the court, his friend said: "Callum began to panic, he looked cold and began to shiver.
"He started to struggle and began to sink. He was waving his arms about until he went under the water."
There was an attempt by one of the other swimmers to reach him, but he too said he began to struggle with the cold water temperature.
The emergency services were called by his friend on the bank but they took almost an hour to find the spot because the caller struggled to identify his location.
Once they were found, the fire service sent out a boat while a police helicopter was scrambled.
The police underwater search team were called and Callum's body was found at 1.25am the next morning at a depth of around 6.5 metres.
He was identified by his finger prints and a postmortem concluded he had died from drowning. There were no reports of alcohol or drugs in his system.
Recording a verdict of accidental death, assistant coroner, Jan Alam, said: "Callum was last seen in the river to be struggling.
"I know there was a significant delay in reaching the location of where they had entered the river, this was not due to the lack of effort by West Yorkshire Police.
"The difficulty in identifying the location was due to the lack of landmarks that were visible from where the boys had entered the river.
"All the evidence suggests this was an accidental death."