Dyfed-Powys Police said on social media that a man had fallen into the River Tawe at Ystradgynlais area, in south Wales, at about 10am on Sunday morning.
The force said he was found dead further along the river in the Trebanos area.
A tweet from the Ystradgynlais neighbourhood policing team said: "A male has fallen into the river at #Ystradgynlais at approximately 10am this morning and has sadly be(en) found deceased further along the river in the Tebanos (sic) area.
"If you witnessed this incident please can you give us a call on 101."
The news comes after Storm Dennis lashed parts of the UK with more than a month's worth of rain in 48 hours, leading to a record number of flood warnings and alerts in England.
Roads and railways were flooded on Sunday morning after torrential downpours and high winds caused by the second storm in just over a week.
The situation was said to be "life-threatening" in South Wales, where the Met Office issued a red warning due to heavy rainfall and flooding risk until 11am.
The Environment Agency's (EA) flood and coastal risk management executive director John Curtin said on Sunday that there were a record number of flood warnings and alerts in force.
The EA said on Sunday afternoon that there been more than 600 flood warnings and flood alerts in place across England.
Mr Curtin tweeted: "Breaking: we now have the most flood warnings and alerts in force (594) in England than any other day on record."
The Met Office said that winds of more than 80mph were recorded across parts of the country, with the highest measuring 91mph in Aberdaron in north Wales on Saturday.
A total of 156.2mm of rain fell at Crai Reservoir in Powys in the 48 hours from Friday to Sunday morning, it added.
The average monthly rainfall for February in Wales is 111.1mm, the Met Office added.
Severe flood warning have been issued for the rivers Neath and Taff in South Wales, as well as the River Teme further north.
Pictures on social media show the Taff bursting its banks and flooding parts of Pontypridd, while rescue workers were using boats to get families to safety after further flooding in nearby Nantgarw.
Gwent Police said that residents of Skenfrith, Monmouthshire, were being advised to evacuate due to the flooding.
At about 11am on Sunday there were 250 flood warnings, meaning immediate action is required, and 344 flood alerts warning people to be prepared, covering an area from Scotland's
River Tweed to the rivers of west Cornwall.
South Wales Police said it had declared a major incident due to the flooding and severe weather.
It said emergency services were dealing with multiple floods and landslides, and have been required to evacuate residents from houses.
Severe flood warning were issued for the Scottish Borders but these were no longer in force by late on Sunday morning.
The Met Office has issued amber alerts, meaning people must be prepared to change plans and protect themselves and their family from the storm, for parts of Yorkshire, Wales, Devon, East Sussex and Kent.
Rail services were suspended across South Wales after tracks were submerged by rain, while the line between Derby and Long Eaton was also closed.
Flooding saw the M54 westbound closed at Telford, along with the A616 around Stocksbridge in South Yorkshire and the A52 between Stragglethorpe and Gamston in the East Midlands, Highways England said.
Relief from Storm Dennis is still some distance away, the Met Office's Mr Dewhurst said, adding that "heavy rain and strong winds" would continue across large parts of the UK on Sunday.
"South Wales will see a lot of rain fall before Dennis moves north later to Scotland and Northern Ireland."
Earlier, the Ministry of Defence deployed British Army personnel to assist people in West Yorkshire areas badly hit by flooding during last weekend's Storm Ciara.
The British Red Cross said that with water levels expected to peak on Monday or Tuesday it was ready to respond across the country.
Its crisis response officer Georgie Timmins said: "British Red Cross have been liaising with relevant local authorities, offering to support people affected by Storm Dennis across the UK.
"We are currently responding in Shropshire, Nottinghamshire, South Yorkshire and Gloucestershire, and we are currently ready to help in Wales, Manchester, Buckinghamshire, Lancashire and Inverness.
"Our volunteers know that when people are caught up in a crisis, one person's needs are different to the next person.
"The storms are expected to continue, and water is anticipated to be at peak levels on Monday and Tuesday.
"It is important people are ready should the worst happen."
Flights have been grounded for safety reasons, with British Airways and easyJet confirming cancellations.
More than 230 easyJet flights in and out of the UK on Saturday were cancelled, while several sporting fixtures were also called off due to the weather.
Two bodies were pulled from rough seas on Saturday, before the worst of the storm hit.
One man was found following a huge search operation off Margate after an early-morning distress call, while