A 24-year-old woman was seriously injured in the blaze and and is in a serious condition in hospital.
Emergency services were called to the house in Achray Place, Milngavie, East Dunbartonshire, at around 7.25am on January 1.
The body of a man was found inside the property. He has yet to be formally identified.
The 24-year-old woman was taken to Queen Elizabeth University Hospital in Glasgow for treatment.
A man and woman, both aged 54, were taken to the same hospital to be treated for smoke inhalation and have since been released.
Police launched a murder inquiry after a joint investigation with the Scottish Fire and Rescue Service determined that the fire was deliberate.
Specialist detectives and forensics experts have been carrying out investigations at the scene and police are appealing for information.
Detective Inspector Martin Fergus said: “This is a truly terrible incident in which a man has died and another woman remains in a serious condition at hospital following a targeted and wilful fire. Local residents are understandably shocked that a man has lost his life within the blaze, particularly given that it occurred on New Year’s Day, a time when families and friends come together and spend time with each other.
“I want to reassure local residents that all is being done to trace the person or persons responsible, and to ensure that they are held to account for their actions.
“Since the fire was first reported, there has been a substantial presence by the emergency services on Achray Place, including the force helicopter. Following the joint investigation which determined the fire was a deliberate act, specialist detectives and forensic services staff have remained at the scene as part of the murder investigation, supported by local uniformed officers.
“Those local officers will also remain in the area to provide reassurance and we would ask local residents to approach those officers with any information they may have.”
Mr Fergus urged anyone with information to contact police.
He said: “It is possible that local residents who were jogging, or walking their dogs, between 0700 hours and 0730 hours, are yet to speak with officers. It is also possible that passing motorists may have witnessed anything which may help our investigation.
“You may have seen someone running away from the house at this time, or perhaps seen someone acting suspiciously in the area. As part of our broader investigation, any information could prove critical in tracing the person or persons responsible for this horrifying crime.”