Sutcliffe, 70, has spent 32 years inside the high-security institution in Berkshire after murdering 13 women and attempting to kill seven more between 1976 and 1981.
Sutcliffe, who has been in Broadmoor since 1984 after he was diagnosed with paranoid schizophrenia following his life sentence in 1981, will continue to have his mental health assessed in prison and could be returned to a psychiatric hospital if there is a change in his condition.
It has been estimated that the move will save the taxpayer hundreds of thousands of pounds.
Dr Ruth Tully, a consultant forensic psychologist at the University of Nottingham, said cost would not have been a factor in the ruling that the serial killer is sane enough to be transferred but that the cost difference was considerable.
Figures show that it costs around £325,000 per year to keep a patient in Broadmoor, compared with around £45,000 per year in a category A prison.
Sutcliffe, a former lorry driver from Bradford, now calls himself Peter Coonan. Most of his victims were prostitutes who were mutilated and beaten to death.
He was given 20 life terms for the murders and was caught when police found him with a prostitute in his car.
They became suspicious and found he had a fake licence plate and weapons including a screwdriver and hammer in the boot.
Before he was moved to Broadmoor, the killer spent three years at Parkhurst prison on the Isle of Wight.
A Prison Service spokeswoman told the Press Association: “We do not comment on individuals.”