The victims of a gruesome double killing in Melbourne’s southeast have been identified as a man is charged over the horrific crime.

Police located the bodies of 39-year-old Athena Georgopoulos and 50-year-old Andrew Gunn inside a home in Mount Waverley on Monday night.

A 34-year-old homeless man was arrested without incident at Westall train station in the early hours of Tuesday morning.

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He has since been charged with two counts of murder and will appear before Melbourne Magistrates Court on Wednesday.

The couple had been together for three years and were expecting a child, with Georgopoulos five months pregnant.

Georgopoulos’ mother attended the scene of the killings on Tuesday and could be heard saying “oh my God” multiple times and screaming about her daughter being pregnant.

7NEWS understands Gunn had been decapitated and his head was believed to be found on a stick.

The nature of Georgopoulos’ injuries is unclear.

A series of cryptic messages were scrawled on the exterior of the home as well as across a fence opposite the property.

The messages included “enough is enough”, “karma has no menu” and references to veganism such as “meat is murder”.

Police say they are investigating if the graffiti is linked to the deaths.

Detective Inspector Dean Thomas said the attack appeared to have been targeted.

“We believe that there is a link between our suspect and the address but we’re just working together at this point to make sense of what that means and what it all looks like,” he said.

“The suspect has arrived at the address and then obviously an altercation has occurred which had led to the male and female being killed and the subject has then left the address.”