John Davis was sentenced to life behind bars after admitting murdering Hazel North, with the minimum term set at the High Court in Glasgow yesterday.
Lady Rae told the 26-year-old: "The circumstances disclose that this was a brutal and prolonged attack. You destroyed a young woman's life while she was in her prime and you have caused indescribable suffering to her family."
Davis showed no emotion as he was led handcuffed to the cells.
Ms North's family were back in court to see him sentenced.
In a statement outside court, her brother Michael North said: "Words cannot describe the feelings we have felt over these past months and although nothing will bring back our Hazel we take consolation in the fact that such an evil individual has been removed from our society.
"The family would like to thank all involved parties who have today prevented a truly brutal person from walking the streets.
"We would like to thank everyone involved who has provided assistance and support for the family during this ordeal.
"We would ask people to try to remember Hazel for who she was, her beautiful smile and not the tragedy that unfortunately took her life."
The court on Tuesday heard how Davis battered the 19-year-old, who was originally from Dunfermline, at his flat in Kilmarnock in March this year.
Davis then hid her remains in a shallow grave in Dean Park in Kilmarnock just 300 yards from his home. He later boasted to a friend: "I done her in and buried her."
It was only during a large-scale search to find Ms North that Davis handed himself in to police.
Ms North's naked corpse was discovered in a "reasonably well-concealed grave" and was wrapped in a sheet and a curtain.
Davis also pled guilty to attempting to defeat the ends of justice.
Ms North died having suffered "severe blunt force trauma" to her head, neck and body.
The court heard on Tuesday that Davis was jailed for a vicious assault using a golf club in 2012 - but had been freed early from prison by the time of the killing.
Lady Rae said it was clear Davis had a "considerable propensity for violence". She said his latest jail term would have been 23 years, but for his guilty plea.
The judge added: "The assault must have been perpetrated over a long part of the day."
By covering up the death, she told Davis: "You must have caused the family untold suffering not knowing where she was or whether she was alive or dead."