Johanna Powell, from Cardiff, was reported missing on Saturday.
The 37-year-old, a BBC Wales picture editor, was on a tourist boat on the Mekong River near Pak Beng.
The Foreign Office told her family on Tuesday local authorities had formally confirmed a body recovered since the incident was hers.
Johanna Powell's brother-in-law Dean Price said her family was trying to arrange to bring her body home as soon as possible.
He said: "We are grateful for all the help, support and kind words that everyone is passing on to us."
Ms Powell, originally from Pontypridd, was with three friends from Wales and one of them was celebrating a 40th birthday. They were part of a group of 10 on the boat, which could hold 25.
Mr Price said the family had been told she was asleep when the boat hit a rock in rapids causing it to tip, take on water and capsize.
Speaking to BBC Wales on Monday, Ms Powell's mother Teresa said: "She got on the plane, she texted me and said 'It's going to be a lush adventure, mum. I love you loads and everything is going to be fine', because I was worried about her going."
Her father Donald added: "The boat hit some rapids apparently and overturned.
"Out of all the ones on board, the rest were lucky and they got to the bank somehow, but Johanna was missing."
The co-owner of the cruise company, Adisak Star, said the boat sank quickly after hitting a rock while travelling though rapids.
"We have been running this for 15 years now and this is the first time this happened and I am sorry this happened," Mr Star added.
BBC Wales Director Rhodri Talfan Davies said: "Jo was such a respected and admired colleague - and I know just how keenly her loss is felt by so many colleagues who had the pleasure and privilege to work alongside her for almost 15 years.
"We are of course offering to support Jo's family in any way we can."
The body of a woman who vanished after a boat capsized on a river trip in Laos, south-east Asia, has been identified, her family says.