Aspiring young Melbourne comedian Eurydice Dixon was stalked for more than 30 minutes by her rapist and killer.
Jaymes Todd followed her from Flinders Street Station, for some 5km across the city, until he unleashed an attack at Carlton North's Princes Park overnight on June 12.
A passer-by found the 22-year-old's body about 3am.
Todd, 19, from Broadmeadows, pleaded guilty to murder, rape, attempted rape and sexual assault in Melbourne Magistrates Court on Thursday.
Dressed in a grey shirt and with a shaven head, he addressed the court when asked to enter a plea.
"Guilty your honour," Todd said.
A summary of events shows Todd first spotted Ms Dixon at the intersection of Flinders St and Swanston Street, central Melbourne, at 11.08pm on June 12.
He followed her up Swanston Street, maintaining a constant distance behind.
"Whenever the deceased slowed down or stopped, the accused made a similar speed reduction," the document read.
As Ms Dixon crossed two soccer pitches and stepped on to a third, she was attacked.
Documents released by the court did not show the exact time of the attack.
Her body was found at 2.50am on June 13 by a passer-by walking home from work.
Todd handed himself in to police later the same day and initially denied any involvement with Ms Dixon.
Ms Dixon's death sparked a national outpouring of grief with a subsequent vigil at the park attracting more than 5000 people.
Then-prime mininster Malcolm Turnbull and Opposition Leader Bill Shorten stood shoulder to shoulder surrounded by colleagues at a vigil held at Canberra's Parliament House.
Federal Labor deputy leader Tanya Plibersek choked back tears as she noted the "shocking" and "terrible" death of Ms Dixon, which shone a light on violence against women.
Ms Dixon had been walking home from performing at a comedy gig at Melbourne's Highlander Club when attacked.
Todd is expected to face the Supreme Court, where he will later be sentenced, on Tuesday.