A homeless man has been charged with murder following the "horrendous" death of 25-year-old Courtney Herron in Parkville.
Ms Herron, who was homeless, was found dead by dog walkers in Royal Park on Saturday morning, sparking a major police investigation.
A 27-year-old man of no fixed address was arrested on Sunday and charged with one count of murder overnight.
He will appear at Melbourne Magistrates Court on Monday.
Police say Ms Herron was slain in a "horrendous bashing" before her body was found. Homicide squad Detective Inspector Andrew Stamper said there was no evidence the attack was sexually motivated.
Ms Herron attempted to call former boyfriend Terrick Edwards in the hours before her death, his sister Nindara Edwards Norris told The Age. She said he now felt responsible "for not being able to offer her a safe place for the night".
The couple had lived in the inner northern suburb of Northcote for "many years" and remained close after separating four years ago, Ms Norris said.
Ms Herron was raised in the northern suburbs, Ms Norris said. She has a sister and brother and was "a part of a beautiful caring Greek-Aussie family".
Ms Herron had suffered "many mental illness issues and recurring homelessness" since the split with her brother, according to Ms Norris.
She said her brother would want Ms Herron "to be remembered for the lovely woman she was and not just another homeless person who died on the streets".
Ms Herron had worked for a government department "a number of years ago", Ms Norris said.
"So to end up homeless and on the street is truly shocking for people to grasp."
Melburnians will gather for a vigil on Friday at 5.30pm at Royal Park, with organisers urging people to "join together" to pay tribute to Ms Herron and reclaim the public park.
"All people deserve safety in this world. Sadly, once again we must mourn the loss of an innocent woman in a place known to so many of us."
Bouquets and heartfelt messages have been placed by mourners at a group of logs behind where Ms Herron's body was found.
The makeshift shrine was continuing to grow on Monday morning, with friends and complete strangers braving the bitter cold winds to make their way across Royal Park and pay their respects.
Annette Graham, 48, didn’t know Ms Herron, but arrived with her 11-year-old son Coulton to place a bouquet of bright yellow roses tied with a red ribbon.
"I wanted to send a message to whoever loved this poor lady, that we are thinking of them, and thinking of her."
Ms Graham, who lives locally in North Melbourne, walks here four or five times a week at 7am and is wondering if it’s still safe to do so.
"It just felt close to home and I just felt’it’s enough. It has to stop. The violence has to stop."
She used to walk at Royal Park at 6am or earlier but said 18 months ago she was followed at strange man and became scared.
A friend of Ms Herron's, who asked not to be named, on Sunday left flowers at the site and wept on the shoulder of another friend.
"She was kind and she was lovely and she was a great friend," she said.
Matt Walsh knew Ms Herron in high school and said she was one of the most kind-hearted people he had ever met.
"[She was] always smiling and joking, trying to make herself and others happy. That's how I'll remember her," he said.
Jadee Craggles posted on Facebook about her anger at Ms Herron's life being taken so young.
"Breaks my heart that we live in such a f—ed up world, nobody deserves this," she said. "It was a pleasure knowing you; even not seeing you in years."
Ms Craggles told The Age she hadn't seen Courtney since high school, and was shocked to hear that she had been struggling.
"She was a beautiful, normal young girl, breaks my heart to hear she was doing it so tough now," she said.
Detective Inspector Stamper said Ms Herron had lived a difficult life, struggling with drugs and mental health issues.
He described Ms Herron as a "vulnerable" member of the community who society had failed to protect.
"This was a young woman who had significant challenges in life. We as a community should be protecting these people and we didn't. We failed on this occasion," he said.
Detective Inspector Stamper said Ms Herron's family was "heartbroken".
"Courtney had had sporadic contact with her family, which is very much part of the challenges that happen when there is a child that suffers drug use and mental health issues … family relationships can be fragmented," he said.
"But I stress, that doesn't mean that families out there don't love their children and their heart breaks for them. We're dealing with a heartbroken family."
The last confirmed sighting of Ms Herron was on May 14 in St Albans when she spoke with police about a minor matter relating to her mental health and drug use.
Police said that towards the end of her life she was transient and interacted with a lot of people, who may be able to help police map out her movements in the final weeks of her life.