Ingrid Wall has taken to Facebook to praise her daughter's humanity and professionalism.
"It's with boundless sadness and shock we have received the news that the remains of our daughter and sister Kim Wall, have been recovered. The breadth of the disaster is still hard to grasp, and there are many questions that need answers," Ms Wall wrote.
"During the horrific days that have passed since Kim disappeared, we have had countless evidence of how loved and appreciated she was, as well as human and friend as a professional journalist."
"From all corners of the world, (we've seen) evidence of Kim's ability to be a person that makes a difference."
"The tragedy has not only affected us and the other family, but friends and colleagues all over the world," Ms Wall continued.
"She has found and told stories from different parts of the globe, stories that must be written.
"Kim travelled for several months in the South Pacific to let the world know what is happening to the population on the islands that sink as a result of nuclear testing. She took us to the earthquake in Haiti, to the torture chamber of Idi Amin in Uganda and the minefields in Sri Lanka. She gave voice to the weak, vulnerable and marginalised people.
"That voice was needed for a long, long time. Now it's been silenced."
Forensic confirmation
The headless torso of a woman found at sea was identified Wednesday as Swedish journalist Kim Wall, thought to have died aboard a Danish inventor's homemade submarine in a grisly case that has gripped public imagination worldwide.
"We have a DNA match between a hairbrush and a toothbrush belonging to Kim Wall and the blood in the submarine and the torso we autopsied yesterday," Copenhagen homicide chief Jens Moller Jensen told reporters.
Ms Wall died after embarking on board a submarine owned by Danish inventor Peter Madsen, 46.
The experienced foreign correspondent was last seen boarding the 18m UC3 Nautilus craft on 10 August with Mr Madsen, who she was interviewing for a feature.
Ms Wall, a graduate of the London School of Economics and Columbia University, was reported missing by her boyfriend in the early hours of 11 August. The submarine sank hours later and Mr Madsen was rescued.
He has since been charged with the manslaughter of Ms Wall.
Madsen's relief
Madsen's lawyer, Betina Hald Engmark, told Danish news agency Ritzau her client was "very relieved" the torso had been identified.
"He wants nothing else than for this case to be cleared up and fully disclosed," Engmark said. "It is in my client's best interest."
Madsen, who has been in custody since August 12, denies the allegations against him.
Wall, a freelance journalist who had reported for The Guardian and The New York Times, was last observed on board the sub with Madsen on August 10.

Danish submarine owner and inventor Peter Madsen. Source: SCANPIX DENMARK
Her boyfriend reported her missing a day later. The same day, Madsen was rescued from waters between Denmark and Sweden shortly before his submarine sank.
Investigators recovered and searched the sunken submarine, which police believe Madsen, 46, sank deliberately.
Madsen, whose website describes him as an "inventepreneur", initially told authorities he dropped Wall off on an island late on the evening of August 10.
But he changed his story several days later when he appeared in court, saying Wall had died in an accident on board and that he dumped the body in the water at an undefined location in Koge Bay.
'Curse' on the sub
A self-taught engineer, Madsen worked with volunteers to build the Nautilus, the biggest-ever private submarine when it was launched in 2008.
But they fell out in 2014-2015 and members of the board transferred the vessel's ownership to him, the submarine's website says.
Madsen had sent a text message to two board members in 2015, saying "there is a curse on Nautilus".
"That curse is me. There will never be peace on Nautilus as long as I exist," Madsen wrote, according to a 2015 post written by the volunteers in Danish on the website.
"You will never have a good feeling inside the submarine... do not throw more lifeblood into that boat."
Wall, a graduate of Columbia School of Journalism, was based in New York and China.
Her friends described her as "invincible", "ambitious" and as "seeing something good in everyone", according to Swedish media reports.
"It is with endless sorrow and dismay that we have received the news that the remains of our daughter and sister have been found," Wall's mother Ingrid wrote in a Facebook post on Wednesday.
Wall had covered news about earthquake-hit areas in Haiti, Idi Amin's torture chambers in Uganda and minefields in Sri Lanka.
"She gave voice to the weak, to the vulnerable and marginalised people," her mother wrote.
"That voice would have been needed much, much longer. But now that will not be so.
- With AFP.