Alicia Williams and David Platt, both 25 and of Ruabon, near Wrexham, were found in the River Clywedog near Felin Puleston.
Ms Williams’s body was found on Wednesday afternoon. Search teams found Mr Platt’s body at about midnight.
Police said they had not found witnesses to confirm reports the pair had gone into the water to save a dog.
The deaths are not being treated as suspicious, but investigations continue and North Wales Police have appealed for witnesses.
Detective Chief Inspector Mark Pierce told reporters the couple were seen earlier walking with five dogs along the river which had been more swollen on Wednesday.
He said the emergency services were called just after 17:00 BST after a member of the public found the woman’s body.
“A search of the area revealed property and a witness who had seen the lady walking with a man in the area with some dogs,” he said.
The incident comes as thousands of people around the UK are enduring problems caused by flooding, although forecasters predict the worst of the rain is over.
Homes, roads and the rail network in northern parts of England and Wales continue to be affected.
BBC North of England correspondent Nick Ravenscroft said residents in York were breathing a sigh of relief after the River Ouse “stabilised”.
Towns and villages along the river Ouse in North Yorkshire were said to have been particularly at risk.
There are still more than 40 flood warnings in place, mostly in the north-east of England, but the number is expected to reduce.
The Environment Agency said about 570 homes and businesses had been flooded across England and Wales since Sunday.
‘Trauma and distress’
Det Ch Insp Pierce said that a search commenced for Mr Platt, who is understood to have worked at a local farm building children’s play pens, and his body was found just after midnight.
“It’s speculation to say whether or not the dogs have gone into the river and one or both of the couple have gone in to save the dogs. We haven’t got a witness to confirm that.”
He said the families of the victims were suffering a “huge amount of distress” as they prepare for formal identification.
“You can imagine the trauma and distress,” he added.
Ms Williams leaves a young daughter.
David Lloyd, who said he knew the dead woman, visited the scene on Thursday.
He said: “She loved animals. She’d do anything for them.”
Workers at businesses near to the scene said they saw a lot of police activity in a nearby car park used by walkers visiting Felin Puleston, which links to Erddig country park.
Michael Morgan “The river has got tremendous power in it”
Michael Morgan, who runs a car wash close to the scene, said he went to investigate on Wednesday after spotting a dog “too good to be a stray” by itself.
He went into the park and saw three more dogs sitting beside a Citroen Picasso, which is thought to have belonged to the couple.
He described the dogs as two retrievers, one a dark golden brown colour and one white, and a small Jack Russell.
Mr Morgan said the two retrievers appeared to be wet up to their heads.
“The next thing we know an ambulance has come down,” he said.
Paramedics asked for directions to a nearby location and after he guided them to the scene along the river they spotted a woman’s body on a sand bank.
He said another man had managed to pull the woman from the water.
He said staff from nearby Erddig Hall, a National Trust-owned property, arrived on the scene along with crews from North Wales Fire and Rescue Service.
Sandra Davies said there was a close-knit community of dog-walkers in the area, adding: “Everybody’s so friendly. It’s very sad.
“It’s such a shock too.”
She said the river was “enormous” when she and her husband Geoff walked their dogs on Wednesday.
She added: “The river was over the banks.
“The banks have collapsed on different occasions and you do get worried about walking too near, especially with dogs who want to run and play, of course.
“It was extremely high yesterday.”
North East Wales Search and Rescue (Newsar) say 20 volunteers were called to the scene on Wednesday following the earlier discovery of the woman’s body.
They checked various locations along the river and surrounding water meadow, said a spokesman.
North Wales Police said anyone with information can call 101.