Warning: This story contains details readers might find distressing

A homeless man in the Australian state of Victoria has been charged with the alleged murder of a pregnant woman and her partner, whose head was decapitated.

Police were called to a unit in Melbourne's south-east on Monday evening where they found the bodies of Athena Georgopoulos, 39, and Andrew Gunn, 50.

Several hours later, police arrested Ross Judd, 34, at a train station about 7km from the scene. He appeared in court on Wednesday, charged with two counts of murder.

Police say the attack appears to be targeted but the relationship between the couple and the accused is not yet known. Police are also investigating graffiti outside the unit with the words "betrayal" and "enough is enough".