Simon Araghi confirmed that Roozbeh Araghi, known as Roozi, died in the accident with his partner Luke Dorsett and Dorsett's sister, Kate Goodchild.
"On behalf of my brother Dory and my family, I confirm the loss of our most loved 'baby' brother Roozi and his partner Luke and our lovely Kate," Araghi wrote. "We appreciate all your support and would prefer to keep some privacy. We are all in shock and mourning."
The fourth victim was Cindy Low, a New Zealand citizen and long-term resident of Australia, whose 10-year-old son survived the fatal accident, according to a statement from a company hired to represent the family.
"The family are traumatized, and kindly request their privacy be respected as they try to come to terms with this tragic loss," the statement said.
All the victims were in their 30s and 40s.
Dreamworld released a statement which stated that, under advice from the Queensland Police Services, the park will not proceed with a memorial planned for Friday.
"The integrity of the Coronial Investigation is of paramount importance and postponing the service will give QPS the time it needs to conduct this investigation," the statement reads.
An earlier statement from Dreamworld PR had said a "private ceremony" would be held for staff, friends and the emergency services Friday.
Updated plans for a service, and the park's reopening, will be released Monday, the statement adds.
Low's son was one of two children who survived when the flume, carrying six people, "flipped" on the Thunder River Rapids Ride on Tuesday.
Brian Codd, assistant commissioner for Southeast Region of Queensland Police Service, described it as "almost a miracle" that the boy and a girl, aged 12, were able to "extricate themselves."
Their flume flipped after it came in contact with another carriage towards the end of the ride, tossing some of the passengers onto the conveyor belt, where they were caught in the machinery, Codd said on Wednesday morning.
The investigation is "intricate" and "very complex," according to Mark Thompson, Detective Inspector with the Queensland Police at the Gold Coast Criminal Investigation Branch.
Thompson said an investigation center had been set up, and that police had taken more than 40 statements. He appealed for anyone who might have been on the ride that day or have relevant photos or mobile phone footage to get in touch.
Thirty detectives and a "significant number of scientific police" and workplace safety experts are investigating the incident, Thompson said, as he cautioned that it would be a "lengthy process."
Tributes paid to victims
Sam Dastyari, a senator for New South Wales, paid tribute to Roozi Araghi in a Facebook post, describing him as "a caring, gentle and sweet soul."
Araghi, Dorsett and Goodchild lived in Canberra, according to Australian media reports.
A statement posted by Australia's Department of Human Services, where both Dorsett and Goodchild worked, said the pair were "well-liked and respected by their colleagues and will be greatly missed."
'Extraordinary loss' for children
"In particular, we would like to acknowledge the tragic circumstances and extraordinary loss for their children."
Dreamworld also also sought to defend the park's safety procedures in the statement, saying that the park was "fully compliant with all required safety certifications.
The attraction, in Gold Coast, about 45 minutes from Brisbane, is the largest theme park in Australia and attracts around 1.8 million visitors each year. It includes animal attractions and more than 50 rides, according to its owner, Ardent Leisure.