The 70-year-old serial killer has spent 32 years inside the high-security institution in Berkshire after murdering 13 women and attempting to murder seven more between 1976 and 1981.
He has been there since 1984 after he was diagnosed with paranoid schizophrenia after being jailed for life in 1981.
Mental health experts have now ruled that Sutcliffe is fit to be moved to prison as he no longer needs any treatment for any mental disorder.
Moving him will have to be approved by the Ministry of Justice.
Sutcliffe 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.
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.
Before he was moved to Broadmoor, the killer spent three years at Parkhurst prison on the Isle of Wight.
A Ministry of Justice spokesman said: “Peter Coonan will remain locked up and will never be released for his evil crimes.
“Decisions over whether prisoners are to be sent back to prison from secure hospitals are based on clinical assessments made by independent medical staff.
“The High Court ordered in 2010 that Peter Coonan should never be released. This was upheld by the Court of Appeal.
“Our thoughts are with Coonan’s victims and their families.”