The deceased man and woman were found inside the home in Mount Waverley, in Melbourne's southeast, on Monday night.
Police had received a call from a concerned neighbour at 9.20pm after hearing yelling coming from the property, Homicide Squad detective Dean Thomas said on Tuesday.
A second call was made, which suggested it was "more urgent", and officers arrived at 9.50pm to find the two bodies.
Local police and homicide detectives were able to identify a suspect, a 34-year-old man, whom they arrested at Westall Railway Station with two large dogs at 1.40am on Tuesday.
Investigators believe he arrived at the home before an altercation broke out, leading to the deaths of the man and woman.
Police were still piecing together the connection between the arrested man and the two deceased people, who are yet to be identified, but it is believed he knew the male occupant at the address.
"We've still got to link that up and, obviously, when we talk to him during the course of the day, that will become more obvious to us," Det Insp Thomas told reporters.
"We are not looking for anybody else in relation to this incident."Â
He said investigators were still examining the crime scene and the extent of the injuries to the deceased pair, saying weapons were used but not a gun.
Det Insp Thomas believed there was no one else at the address during the incident, nor was it a robbery.
"Of course, that's very traumatic. It's not something that's pleasant, but it is something that our members (are) prepared for. But obviously they weren't expecting that last night," the homicide squad boss said.
Counselling and support will be offered to residents, but Det Insp Thomas has reassured the community that the incident appears to be a "targeted attack".
"I urge those in the community to take that on board and understand that it's very, very sad that it's occurred, but it appears to be very contained," he said.
Det Insp Thomas said the suspect, who may be homeless, was arrested peacefully at the train station and urged anyone in the area who had seen the man to contact CrimeStoppers with any information.
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