Zhi Min Chen, 44, choked Tracey Wylde to death at her flat in Barmulloch in November 1997.
The body of the 21-year-old mother-of-one – who had been working as a prostitute – was found the next day.
Chinese-born Chen, who admitted the murder last month, was arrested last summer after his DNA was taken following an alleged assault.
Lord Arthurson told him: “You committed a brutal, cowardly and murderous attack on a vulnerable young woman in her own home.”
He added: “You should be under no illusions concerning the damage and trauma that your murderous attack that day upon Ms Wylde has caused and indeed has continued to cause down the decades and beyond to her family.”
Chen, who was 22 at the time of the murder, stood with his head bowed in the dock as he was sentenced to life in prison.
He must serve at least 20 years before he can apply for parole.
Lord Arthurson said Chen, who had no previous convictions, had enjoyed more than two decades of “undetected freedom” after the killing, during which time he had started a family and a business.
Speaking outside court, Ms Wylde’s sister, Bernadette McCash, described the sentence as “a slap in the face”.
She said: “I don’t feel it is enough time.
“As a family we are really disappointed in the sentence.
“He ran for longer (than 20 years). He hid for longer.”
Police had described Ms Wylde as having a “turbulent background” and said that she had been a sex worker in Glasgow at the time of her death.
She had been raised by her grandparents before moving into her own flat and giving birth to her daughter in August 1994.
The High Court in Glasgow heard Ms Wylde had gone into Glasgow city centre on 23 November 1997, and was last spotted on CCTV in the city’s red-light area at about 03:20 the next morning.
Prosecutor Steven Borthwick said neighbour Mary McAnemy heard arguing in Ms Wylde’s flat. The last thing she heard was the door being slammed shut and keys being rattled.
Ms Wylde’s body was discovered after she failed to show for an appointment at a support group.
Lord Arthurson said the minimum jail term would have been 22 years, but for the guilty plea.