Sentencing Stephen Griffiths for his "wicked and monstrous" crimes, Judge Mr Justice Openshaw told him he would never be released from prison.
Griffiths, 40, murdered Suzanne Blamires, Shelley Armitage and Susan Rushworth, who all worked in the red light district near his home in Bradford, West Yorkshire.
He was caught when a caretaker at the flats where he lived saw horrific CCTV footage of Ms Blamires's final moments.
When he was arrested Griffiths told police "I've killed loads" and claimed he had eaten some of Ms Blamires's flesh, adding: "That's part of the magic".
Griffiths stood in the dock to enter his pleas surrounded by five security guards. Dressed in a grey tracksuit, he said "yes" when asked to confirm his name.
He said "guilty" in a quiet voice when the clerk put each of the three murder charges to him.
Mr Justice Openshaw told the court the defendant's mental health had been carefully examined and there was "no question that he was fit to plead".
Prosecuting, Robert Smith QC said it was the job of the caretaker at the housing association development where he lived to review CCTV footage each morning.
On May 24, as he watched the recordings at 8.30am, he made his grim discovery.
Footage from camera 14 showed Ms Blamires running out of Griffiths's flat with her killer in pursuit.
She was then seen being dragged along the floor by her leg by Griffiths.
Mr Smith said Griffiths was seen to have something in his hand.
The woman was then shot with a crossbow before Griffiths "gestured" by holding a finger up to the camera.
Mr Smith told the court how Griffiths told arresting officers: "I'm Osama bin Laden".
The prosecutor said once in a police station he told officers: "I've killed a lot more than Suzanne Blamires - I've killed loads.
"Peter Sutcliffe came a cropper in Sheffield.
"So did I but at least I got out of the city."
Mr Smith said Griffiths told police Suzanne Blamires - who he knew as "Amber" - was "gone".
He said he told officers he had "eaten some of her" adding: "That's part of the magic".
Griffiths also told the interviewing officers he was "only going to talk about five Bradford cases".
Family members sobbed as the prosecutor outlined details of the murders.
Mr Smith said Griffiths had admitted killing Ms Blamires in the flat and dismembering her by hand. He said power tools had been used on the other victims.
"It was just a slaughterhouse in the bathtub," Griffiths told officers.
Mr Smith told the court 81 different pieces of Ms Blamires were found in or by the River Aire in Shipley.
He said a broken knife and a crossbow bolt were embedded in her severed head.
The prosecutor said the head had had its skin removed as well as its nose and ears.
One of the feet was found in the same rucksack as the head.
Numerous other pieces of Ms Blamires were found in a holdall recovered from the river, including her hands.
As Mr Smith read out more and more gruesome details, Griffiths sat motionless in the dock, with his chin on his chest, staring down.
The prosecutor said Ms Blamires's body was reconstructed and pathologists were able to piece together how she died.
They decided she had not been sexually assaulted.
The court was told Griffiths possessed a number of "disturbing video recordings and images"
One image showed Ms Armitage lying dead in the bath. Another, unidentified victim, was lying bound on the living room floor with green twine.
At one point video footage showed the hands of the defendant fondling the victim's bottom.
Mr Smith said furniture and the walls in the flat were splattered with blood.
There was evidence that Ms Rushworth and Ms Armitage had bled in the flat, he said.
Ms Blamires's clothing was found in a bin and revealed a stab cut in the back of the clothing.
Scientists concluded she had been stabbed in the back and a crossbow had entered her left breast.
The court heard that Griffiths was picked up on CCTV carrying a rucksack in the Bradford and Shipley areas.
He told police he was studying for a PhD in homicide, had "cut himself off from society" and that a "civil war" was going on in his head.
Griffiths, who pleaded guilty to the murders at Leeds Crown Court today, showed no emotion as the judge imposed the whole life tariff.
Mr Justice Openshaw told the court: "The circumstances of these murders are so wicked and monstrous they leave me in no doubt the defendant should be kept in prison for the rest of his life."
He added: "His pleas of guilty have been entered without any remorse at all.
"He has never said he regretted his actions or said in even the most perfunctory way he was sorry."
A silent Griffiths was then led from the court by guards.