The 40-year-old is appearing at Bradford Magistrates' Court having been charged with the killing of Suzanne Blamires, Susan Rushworth and Shelley Armitage within the city's red light district in the past 11 months.
Miss Blamires, 36, was executed with a crossbow and "severely dismembered" before some of her remains were dumped in a river.
Her mother said last night that her daughter had "taken the wrong path" in life but that she was a "much-loved" family member.
Nicky Blamires, 54, said: "Nobody deserves this. All these girls were human beings and people's daughters."
The Daily Telegraph can disclose that Mr Griffiths had previously been treated for psychiatric problems at the high-security Rampton hospital.
The search continues for the bodies of Miss Rushworth, 43, and Miss Armitage, 31, who disappeared from Bradford's red light district – the same streets once stalked by Peter Sutcliffe, the Yorkshire Ripper. Officers were searching waste ground yesterday and planned to trawl landfill sites. Forensic searches at Mr Griffiths's one-bedroom flat in Holmfield Court are expected to continue for up to three weeks.
Police were alerted on Monday by a caretaker who was reviewing CCTV footage from the block of flats. The recording showed a man and a woman go into a flat in the early hours of Saturday before she ran out fully-clothed two minutes later.
The man followed and beat her to the floor, then produced a crossbow before shooting a bolt through her head and dragging the body out of view. He was later seen carrying bin liners and a rucksack at various times over the weekend.
On Tuesday, a day after police had arrested Mr Griffiths, parts of Miss Blamires body were found in the River Aire in nearby Shipley. It is understood that a severed head was discovered in a rucksack.
Detectives may widen the inquiry in the next few months to study links with the murder of three other women in the area, but they are not formally linking the cases to the current inquiry at present.
Peter Mann, of the Crown Prosecution Service, said there was sufficient evidence to charge Mr Griffiths with all three murders. He will appear at Bradford magistrates' court this morning.
A man accused of being a serial killer has appeared in  magistrates court in West Yorkshire today charged with three counts of murder. 40-year-old Stephen Griffiths is accused of killing Suzanne Blamires, 36, Susan Rushworth, 43, and Shelley Armitage, 31, all prostitutes.

Griffiths, a former van driver with a degree in psychology and studying for a  in criminology, gave his name as "Crossbow Cannibal" when asked. He has been in police custody since Monday when police were alerted to a  recording that appeared to show a murder.

A caretaker had been reviewing footage from the flats where Griffiths lives when he saw footage of a woman and a man enter a flat early on Saturday morning. Two minutes later, she ran out and was followed by the man, who beat her to the ground and shot her in the head with a crossbow. Over the course of the weekend, the man was seen several times with bin bags and a rucksack.

On Tuesday, the day after the arrest of Griffiths, Blamires' remains were found in the  in nearby . She had been cut into several pieces and her head was located in a rucksack. Police continue to search for the other two alleged victims; Rushworth has been missing since June last year and Armitage vanished in April.

Police have searched much of Bradford's , where Griffiths' third-floor flat is located. Forensic investigations at the flat are expected to last around three weeks. There are plans to search landfill sites for bodies, and police may yet expand the inquiry to cover three more cold cases, although at present they have not been linked to the current inquiry.

Sniffer dogs have been used throughout the city, and police have been taking away plastic evidence bags. Some alleyways remain closed off. Police charged their suspect yesterday.

Griffiths was known as "the lizard man" in his block of flats owing to his habit of walking his two pet  in the area. One neighbour is reported to have quoted him as saying he was studying for "a PhD in murder and ," and he has spent time in a high-security psychiatric hospital. During his five-minute court appearance he did not enter a plea, kept his head bowed and fidgeted with his cuffed hands. He said "Here, I guess," when asked for his address.

As he stood in the glass-fronted dock, guarded by three security officers, he was watched by the families of Rushworth and Armitage, who were accompanied by police family liaison officers. Blamires' family chose not to be present, but the victim's mother Nicky Blamires, 54, has told the press that Suzanne was a "much-loved" family member even though she "went down the wrong path and did not have the life she was meant to have." "Nobody deserves this," she said. "All these girls were human beings and people's daughters."

Griffiths' morning court appearance was followed by a second one this afternoon, at Bradford . This time, he confirmed his name without incident. He was remanded into custody until next month, when he will appear in court again.

British media has been quick to compare the case to , dubbed the "Yorkshire Ripper". Sutcliffe was a Bradford killer responsible for thirteen murders and seven attempted murders, including several prostitutes. Since his 1981 conviction he has spent most of the last three decades in  high-security psychiatric hospital near London.