The 25-year-old was with a friend in the Kirkstall area when he decided to swim at around 8.30pm on Saturday night.
His friend contacted emergency services when he vanished beneath the surface and failed to emerge.
A large-scale search and rescue operation involving both police and the fire service began and his body was recovered in the early hours of Sunday morning.
He was pronounced dead at the scene and his family have been informed.
West Yorkshire Police have issued several warnings over the dangers of swimming in rivers, reservoirs and quarries during the current spell of hot weather.
A teenage girl was taken to hospital after getting into difficulties while swimming in East Ardsley Reservoir with a group of youths on Friday night, and there have also been teenagers gathering at the Old Brickworks in Swillington to swim in the disused pit.
Temperatures in rivers and reservoirs are often extremely low even during the summer months and swimmers can enter cold water shock, a leading cause of drownings.
There are also hazards such as dangerous objects below the surface of the water that may not be visible from the shore and which can trap and injure swimmers.
It can also be difficult to exit the water in quarries and rivers which have steep sides and no steps or ramps provided.
In addition, the water in disused quarry pits can still contain the remnants of toxic chemicals.