Knife-obsessed loner Colin Ash-Smith, 46, must serve a minimum of 21 years in prison for the “barbaric” attack.
Ash-Smith, who is already serving life for attacks on two other women, stabbed Claire to death in an alleyway near her home in Greenhithe, Kent, four days after she turned 16.
The former milkman was first questioned as a suspect in 1995 and Claire’s parents, Linda and Cliff, were convinced he was the killer.
But they died before he was charged with her murder.
Judge Mr Justice Sweeney said Claire had an “engaging and lively personality” and was “extremely popular, with a wide circle of friends”.
He told Ash-Smith: “I have no doubt that this was a premeditated murder that you carried out because of the feeling of power that it gave you.
“In so doing, you not only ended Claire’s young life which was so full of promise, but you also caused unbearable grief and upset to her family and friends.
He added: “This was a premeditated murder. Your intention was to kill. You took a knife to the scene for the purpose, and Claire was vulnerable by reason of her circumstances.”
Ash-Smith chose not to attend Inner London Crown Court today to hear his fate.
Mr Justice Sweeney said he had to sentence Ash-Smith on the basis of the law as it stood at the time of his murder, even though there were no mitigating factors, so he escaped being handed a “life means life” sentence.
Around a dozen of Claire’s schoolfriends packed into the public gallery to hear the sentence read out.
The judge commended Claire’s family and friends who sat through the trial, and the police for their work in bringing her killer to justice.
He said: “I would also like to commend the members of Claire’s family and her friends who have attended this trial for the dignified way in which they have conducted themselves.
“And I express my sorrow for the burden they have had to carry for many years at Claire’s untimely loss.”
Ash-Smith was branded “pure evil” by police, while prosecutors said he got a “warped pleasure” out of attacking women.
Claire was stabbed at least nine times as she as she walked to her friend’s house in Greenhithe to talk about college options.
The Dartford Grammar School pupil, known to her friends as Tilt, had just finished her mock GCSEs and dreamt of becoming a firefighter.
But her life was cut tragically short when Ash-Smith, whom she knew through the local British Legion club, pounced on her on January 18 1993.
Ash-Smith attended her funeral with his councillor parents a month later in the same beige jacket he wore when he killed her.
His mother Diane, a Labour councillor and later the local mayor, provided him with a false alibi, claiming he was out leafleting with her when Claire was killed.
The trial heard chilling details of how Ash-Smith killed Claire as part of a “spree” of attacks on females across Kent.
A self-confessed “animal” with “no moral compass”, he was plagued by a hatred of women who he felt “humiliated” him.
He went on midnight walks armed with knives hunting for victims, and bragged about his attacks in diaries.
Asked why he attacked, he said: “I wanted to feel empowered, that I had control over someone, that I wasn’t a doormat.”
In 1988, he attempted to rape and murder a young mother in a quarry.
And in 1995 he struck again, stabbing 22-year-old Charlotte Barnard 14 times just yards from where he killed Claire. In 1996 he was handed three life terms and ordered to serve 15 years for the attacks.
He was charged with Claire’s murder earlier this year, on the day he was due to be considered for release by the Parole Board.