The darkness is nearly over for Kylie Maybury's mother, who wept with relief after a man pleaded guilty to murdering her six-year-old daughter in 1984.

In the hours after Black Knight won the Melbourne Cup, Gregory Keith Davies, then 42, abducted Kylie from an East Preston street as the little girl walked home from a shopping errand.

He sexually abused her, then killed her and left her body in a gutter.

Davies, now 74, on Monday pleaded guilty to one count of murder and one of rape in Melbourne Magistrates Court, giving Kylie's mother, Julie Ryan, relief at last after decades of torment.

A charge of false imprisonment was withdrawn.

"It's been 33 years and he's put me through hell," Ms Ryan said outside court.

"I didn't [expect the guilty plea] and I'm so totally over the moon that he's done it.

"It's just made life so much easier.

"And all the other victims out there who have lost their children, I can understand exactly where they are and where they stand."

On November 6, 1984, Kylie, her little sister and their mother had been at a pub with a neighbour for the big race and afterwards went back to the friend's flat for a cuppa.

While there, Kylie was asked to go to a nearby shop to buy sugar.

With a handful of small change and her Strawberry Shortcake handbag, she left, with instructions to buy the sugar and come straight back.

According to documents released by the court, Kylie bought the sugar about 5.30pm and was seen – in her red skivvy and fawn pants – by another woman, who was concerned the little girl didn't know where she was going.

About 10 minutes after Kylie left the flat, her mother became concerned and went looking for her.

Within the next two hours, police had been called and a search had been organised.

About 12.45am the next day, Kylie's body was found in a gutter, about 650 metres from her home.

Davies' admissions came on the first day of his committal hearing, before any evidence had been heard, and came as a shock to Ms Ryan, who had not expected him to plead guilty.

She will now be spared from giving evidence in court about her daughter's disappearance and death.

Ms Ryan tearfully embraced supporters after the short hearing and, outside court, said Davies' admissions would let her and her family "live our lives again".

"It makes a lot of difference," she said.

"It makes [things] calmer.

"We all can move on and we don't have to look in the darkness again.

"The darkness is nearly over."

In 1984 Davies was a houseman at the Windsor Hotel and was living three streets away from where the Maybury girls lived.

Two days after Kylie's body was found, Davies was spoken to by police investigating the murder.

He told them he had been at a barbecue on Cup Day and returned home in his white Holden station wagon about the same time Kylie went to the shop, but that he spent the night at home alone, as his mother and sister stayed with a relative.

He denied having ever interacted with Kylie, though Ms Ryan told police she believes she once delivered pamphlets to his address.

As DNA technology advanced in the years after the murder, samples taken from Kylie's clothing were analysed in 1995 and again last year, eventually leading investigators to Davies, who was living in Waterford Park, north of Melbourne.

He initially denied the charges when arrested last June, but his admissions mean he will front the Supreme Court on Tuesday, when a date for a plea hearing will be set.

Davies arrived in Waterford Park, near Kilmore, in the late 1990s. His brother, Alf, had been doing handiwork for a widower, and been living in a caravan at the rear of the house.

Alf eventually asked if Davies could also live there, and the pair helped paint the house, among other chores. When Alf died of throat cancer a few years later, Davies kept living there. 

A short time after that, he married the widower – despite being 17 years her junior.

A relative of Davies' wife said the 90-year-old had moved out of the house after his arrest, partially because she had relied on Davies to help care for her. The relative had not spoken to Davies' wife on Monday about the guilty plea.

On the day he was arrested last June, Davies' wife was "completely devastated", a relative said at the time, "and she's in two minds. She doesn't want to believe it, but knows she has to believe it too."

Neighbours told Fairfax Media that Davies had always made them feel uneasy.

With Nino Bucci