John Davis carried out a brutal and sustained assault on Hazel North at his flat in Kilmarnock, Ayrshire, in March.
Davis then hid the 19-year-old's remains in a shallow grave and later boasted to a friend: "I done her in and buried her."
It was only amid a huge search to find Ms North that Davis handed himself into police - having earlier fled to try and join the Foreign Legion.
The 26-year-old yesterday pled guilty to the murder as he appeared at the High Court in Glasgow. No motive was given in court for Ms North's murder.
It emerged Davis had been back on the streets only a couple of months, having been jailed in October 2012 for 33 months for a vicious golf club assault. His jail term was not due to expire until May 9 next year.
The family of Ms North were in the courtroom to hear details of her death and the discovery of her body.
Prosecutor David Nicolson told how Ms North had started dating Davis in May 2012 after meeting in Stranraer. The relationship was described as "on-off" at the time of the murder.
Ms North, originally from Dunfermline, Fife, had last spoken to her parents on February 28, which was also the same day she was last seen.
Mr Nicolson said this was "completely out of character", adding: "It was unusual for her not to be in contact with her family."
It eventually led to a large-scale missing persons inquiry being launched on March 19. It attracted widespread publicity when Ms North's relatives set up a Facebook appeal. The suspicion soon fell upon Davis.
His friend James Christie told detectives of a conversation he had with the killer on March 18.
Mr Nicolson told the court: "Mr Christie said both he and Davis had been in his home and when he asked him where Hazel was (Davis) responded he had 'done her in and buried her'."
Police eventually searched Davis's flat in Northcraig Road, Kilmarnock on March 21. No-one was home, but police found a mud-splattered spade.
On March 23, as the search for Ms North continued, Davis suddenly turned up at Kilmarnock police station with a suitcase. He demanded to talk to officers and on his way to an interview room, he blurted out: "Hazel is dead and I'll show you where she is."
He later added she had "passed on March 9" and eventually directed police to Dean Park, just 300 yards from his flat.
Advocate depute Mr Nicolson said: "He pointed out an area of the ground and said Hazel North was 'in there'.
"He continued: 'This is helping me. I realise what I did was wrong and I'll face the music from here'."
After a huge search, Ms North's naked corpse was discovered in a "reasonably well concealed grave" and was wrapped in a sheet and a curtain.
It is thought the body had lain there for about two weeks.
The court heard Ms North died having suffered "severe blunt force trauma" to her head, neck and body. Her list of injuries included massive bruising and multiple fractures - including to the jaw, eye socket and 14 to the ribs.
It emerged after Davis was held that he had got in touch with hairdressing lecturer Mark Pawsey shortly after he killed Ms North. They had previously met in Blackpool - but had not been in touch for about two years. He asked if he could stay with Mr Pawsey in London before he went to France to join the Foreign Legion.
Judge Lady Rae is due to sentence Davis - who also admitted attempting to defeat the end of justice - today.
None of Ms North's family commented after the hearing.