Schoenborn asked for the move at a review board hearing in February, saying his mother and other family members could visit him in the Selkirk Mental Health Centre facility near Winnipeg.
The review board panel had recommended the transfer, but the responsible B.C. justice official declined consent.
"Ultimately, the assistant deputy attorney general, the head of the branch, reviewed the matter and concluded that in the interests of public safety, it was best that Mr. Schoenborn not be transferred at this time," said Neil MacKenzie, spokesman for the branch.
He will remain at the Forensic Psychiatric Hospital in Port Coquitlam, B.C. No request for the transfer was made to justice officials in Manitoba.
An official at the B.C. Review Board said the board had not been advised of the decision, and therefore had no comment.
Schoenborn was found not criminally responsible by reason of mental disorder for the April 2008 slayings of 10-year-old Kaitlynne, eight-year-old Max and five-year-old Cordon in their Merritt, B.C., home.
He stabbed his daughter and smothered his sons before fleeing, only to be found a week later dehydrated in the woods not far from the crime scene.
The statement issued Monday noted the considerable public attention the case has received.
Dave Teixeira, a spokesman for the murdered children's mother, Darcie Clarke, said the family was "absolutely ecstatic" with the decision.
"The concern was that he was going to be transferred to Manitoba, which means that for his annual hearings the family would have to raise money to go and contest the hearing," he said. "Because he's not in the criminal justice system, there's no victims' fund. There's nothing for the family. They would have to go, and fly, and pay all of those expenses."
Clarke also had concerns because she has family living in close proximity to the facility in Manitoba, Teixeira said, as well as concerns about the location and physical layout of the facility in Manitoba. The Selkirk hospital is surrounded by an open field.
"Because Schoenborn has survival training — after he committed the three murders he ran away and hid in the bush for 10 days — the concern was that he could easily escape there," he said.
During erratic testimony at his trial, Schoenborn, 40 at the time of the slayings, said he killed the children to protect them from what was later described as an imagined threat of sexual abuse. The Crown claimed the murders were revenge on Clarke for leaving her husband.
The case sparked outrage, and anger was renewed when 14 months after he was found not criminally responsible, the B.C. review board granted Schoenborn the possibility of supervised day trips into the community.
Two weeks later, amid a public outcry and after learning that Clarke lived in the city where Schoenborn is incarcerated, the board held another hearing at which Schoenborn unexpectedly withdrew his request. In the interim, he suffered a severe beating by another patient.
Schoenborn has been the focal point of a federal government effort to change laws affecting mentally ill offenders.
He was cited by Prime Minister Stephen Harper when he announced legislation earlier this year creating a "high-risk" designation for not criminally responsible offenders. Such offenders will face a mandatory review every three years, rather than every year.
Schoenborn is scheduled to appear before a review board panel for his annual hearing before the end of February 2014.
Teixeira said the family hopes the new legislation means it will be his last for a few years.
"That's given her some great hope that upon the next hearing ... that when Allan's found yet again to be high-risk that he'll be put away for three years instead of one year," he said. "She feels she's being heard."