Davies was told by a judge at the Old Bailey that he faced a minimum term of 23 years for killing Rasta.
Judge Richard Hawkins said he believed the attack had "sexual motivation and involved sexual conduct."
Davies, of Mitcham, south London, told a trial he had been chain-smoking cannabis and was "very stoned" on the day the Estonian died.
Rasta went missing in July 2006 and her body lay undiscovered in a copse for 12 days after she was killed.
Davies was found guilty on last Nov. 14 of murder and perverting the course of justice by burying the body to avoid detection.
Jurors were told that evidence pointed to a "sexual motive" for the killing. Detectives found a kitchen knife covered in blood at the home jobless Davies shared with his mother.
The name "Gaz" was carved into the branch of a tree near where the naked body of Miss Rasta was found after police were alerted by a dog walker.
The court heard that Rasta, who was "fit, athletic and quite strong," lived near Mitcham Common and would often jog and sunbathe there.
She disappeared on July 4, a day after working a shift at the LK Bennett concession at Harrods in Knightsbridge.
Mark Ellison, the prosecutor, said Davies was "something of a loner" who spent much of his time on the common alone or with his black Staffordshire bull terrier.
Precisely what happened to Miss Rasta was unclear as her body lay undiscovered for 12 days and decomposed so badly that a pathologist was unable to establish the cause of death.
The victim's mother, Sirje, told the court in a victim impact statement that her daughter wanted to become a social worker and that "helping others would be her mission in life."
Davies has two previous convictions as a teenager for knife possession, at the time telling police he had the blades to defend himself from bullies.
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