Mr Justice Gross said: "It is right you should spend your whole life in prison."
He added: "This was a targeted campaign of murder."
Wright was being sentenced a day after being convicted of the killings of five prostitutes following a six-week trial at Ipswich Crown Court.
A jury took less than eight hours to find him guilty of murdering Gemma Adams, 25, Tania Nicol, 19, Anneli Alderton, 24, Paula Clennell, 24, and Annette Nicholls, 29.
Wright, 49, a former steward on the QE2 who lived in Ipswich, Suffolk, had denied any involvement in the women's deaths.
Jurors heard that the naked bodies of the women, who all worked as prostitutes in Ipswich, were found in isolated locations near the town between December 2 and December 12 2006.
Detectives launched an investigation after Miss Nicol vanished in late October 2006.
Prosecutors said Wright, who lived in the red light district, "systematically selected and murdered" women after stalking streets around his home.
A pathologist said the evidence showed all the women had been choked or strangled.
The judge told Wright a life sentence was mandatory but he had to decide whether he should be eligible for parole or not.
Mr Justice Gross said he had reached his "sombre conclusion" after considering the facts and arguments put forward by prosecution and defence lawyers.
"I must pass a sentence which meets the justice of the case," he said.
"In my judgment upon reflection it must be a whole life term."
Bowing his head occasionally, Wright sat emotionless as prosecutors asked the judge to ensure he is never allowed out of jail.
Wearing a dark suit with an open-collar white shirt, Wright listened intently as he waited to learn his fate.
Many relatives of the five victims of his killing spree packed into the public gallery of Court Number One at Ipswich Crown Court to witness the proceedings.
Also among them was Wright's brother David and sister Jeanette who both sobbed throughout while sitting arm-in-arm.
Five of the jurors who convicted Wright of his crimes yesterday turned up at court to see the sentence handed down to him.
Wright, sipping water periodically, watched prosecutor Peter Wright outline the argument for him to spend the rest of his life behind bars.
Mr Justice Gross said Wright had targeted vulnerable women.
"Drugs and prostitution meant they were at risk," the judge told Wright.
But neither drugs nor prostitution killed them. You did."
He added: "You killed them, stripped them and left them... why you did it may never be known."
The judge said the case met the legal requirements for a whole life sentence because the murders involved a "substantial degree of pre-meditation and planning".
He also pointed to the "macabre" way in which Wright arranged two of the women's bodies in a crucifix shape.
As Mr Justice Gross said he should serve a "whole life" jail term, Wright stared ahead and showed no facial expression.
Immediately after the judge completed his sentencing, Wright removed the headphones he has worn throughout the trial and went to get up from his seat.
While the judge praised the prosecution, Wright was led out of the dock by the two prison officers who sat either side of him.
Looking at the floor, he made no eye contact with anyone else in court as he was led away to start his life sentence.
There was no reaction from the relatives in the court, many of whom tried to crane their necks to see the dock as Wright was taken away.
Wright's defence team said they would be considering whether there were grounds for an appeal, but stressed this was routine in all criminal cases.
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