Lewis Howlett, aged 25, was a teacher at The Farnley Academy, in Leeds.
He died after going swimming in a stretch of the River Aire off Redcote Lane in Kirkstall, police confirmed.
Lewis' parents said they were 'devastated' at the loss of their son.
A statement from his family said: “We are devastated by the sudden loss of our son Lewis.
“He was loved by all who knew him and our lives will never be the same without him.
"The family now ask for privacy so we can grieve."
Police and partner agencies are now warning of the dangers of swimming in open water following Lewis' tragic death.
Shortly after 8.30pm on Saturday, friends who had been with Lewis contacted police to say he had gone missing while swimming.
Emergency services carried out a search of the area and his body was recovered from the water in the early hours of Sunday morning.
Lewis was pronounced dead at the scene and his family have been informed.
There were no suspicious circumstances and the Coroner’s Office has been notified.
Detective Inspector James Entwistle, of Leeds District CID, said: “This is an absolutely tragic loss of the life of a young man, and his family and friends have been left completely devastated.
“Our sympathies are very much with them, and with the school community, at what will be an understandably difficult time.
“Although we are still working to establish the full circumstances of this incident to assist the Coroner, his death does appear to starkly illustrate the dangers of swimming in open water.
“We hope that people will recognise the risks and the tragic consequences that can occur and avoid swimming in open water, no matter how tempting it might be in the hot weather.”
Police and Yorkshire Water issued a warning on Saturday morning following an incident where a 12-year-old girl was taken to hospital after getting into difficulty while swimming at Ardsley Reservoir in Leeds.
Local neighbourhood policing teams have also dealt with a number of incidents over the weekend with groups congregating at rivers and reservoirs.
West Yorkshire Fire and Rescue Service’s District Commander for Leeds, Andy Farrell, said: “We are very saddened to hear about this tragic loss of life and we extend our deepest sympathies to the family and friends of Lewis Howlett.
“With the recent good weather it’s tempting to go for a swim in rivers, lakes or reservoirs but you can quickly get into trouble with devastating consequences.
“We urge people to be extremely vigilant around open water. Even if you consider yourself to be a strong swimmer, you can suddenly get out of your depth or be taken unawares by hidden undercurrents or cold water shock.”
Councillor Debra Coupar, Leeds City Council’s executive member for communities, said: “It is heart-breaking to hear that a man has died in these circumstances and our thoughts are with his family and friends at this incredibly sad time.
“We understand that it can be tempting to go for a swim on a summer’s day, however, swimming in open water brings many unnecessary risks.
"We urge people to think twice about entering unsafe waters.”
Further safety advice and information is available from the National Fire Chiefs Council water safety campaign Be Water Aware https://www.nationalfirechiefs.org.uk/Be-Water-Aware
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