David Smith, described by the judge as "extremely dangerous to women and likely to remain so", murdered and mutilated 21-year-old Amanda Walker last April, and buried her in a shallow grave at a Surrey beauty spot.
Smith was cleared six years ago at the Old Bailey of the almost-identical murder of another prostitute, Sarah Crump.
In a statement issued after Smith was jailed, Ms Crump's mother, Pat Rhodes, said: "We are very relieved with this result today. Nothing will bring Sarah back, we know that, but we feel there has been unfinished business while Smith has been free."
She sent condolences to Miss Walker's family.
The Recorder of London, Judge Michael Hyam, told Smith it was evident he killed Ms Walker "to satisfy your perverted sexual obsession. You are without pity or remorse".
Smith, 43, from Hampton, west London, had denied murdering Miss Walker.
Police may now interview him about other unsolved attacks on women all over the country. Smith's details, together with those of Ms Walker's murder, have been circulated to all UK forces.
Miss Walker's body was found near the Royal Horticultural Society gardens at Wisley in Surrey nearly six weeks after she disappeared.
Smith had picked up Ms Walker in Paddington. She had been trying to give up prostitution. Smith had already been arrested by the time her body was discovered.
While in prison awaiting trial for Amanda Walker's murder, Smith boasted of murdering her to his cell-mate, Stephen Williams.
Williams, himself a sex offender, was appaled by what he had heard and told police.
Miss Walker's family, from Swarcliffe, Leeds, did not attend Smith's trial.Reuse content