Adams,64,who has maintained his innocence,did not appear to react when the sentence was delivered. He will be eligible for parole in 2031.
In delivering his sentence,Justice Richard Button said it was regrettably a forlorn hope that Adams would ever reveal where he had put the body of Ms Wallace so she could receive a proper burial.
Ms Wallace,33,a well-liked theatre sister who worked at Hunters Hill Hospital,met Adams,then 31,at the Alpine Inn on the lower north shore in the early hours of a Saturday in September 1983.
The last time she was seen was getting into Adams'car after he offered her a lift home from the wine bar after falsely claiming that he was a police officer.
Adams choked Ms Wallace to death while attempting to rape her,then stored her body in his car before trying to remove all traces of her.
"This offence against a young woman in the prime of her life,simply for the sexual gratification of the offender,cannot be assessed as anything other than extremely grave,"Justice Button said.