Ambulance crews were called police to an apartment in Auchinleck House, Sidbury Heights, Tidworth at 1.20pm on Saturday.
They found the body of the man, thought to be in his 30s, in one room and those of two young children in another room.
The man has been confirmed to be 36 year old Graham Gordon Anderson. He was identified by a close relative.
The investigation is continuing today. The property is cordoned off and an examination of the scene is being undertaken by crime scene investigators and a pathologist.
A post mortem examination of Mr. Anderson is being conducted in Flax Bourton near Bristol. The post mortem of the two boys will take place in Southampton over the coming days. An incident room has been set up at Marlborough Police Station.
Detective Chief Inspector Ian Saunders is leading the investigation.
Officers have been speaking to witnesses and residents but are appealing for the public to come forward if they can help with any information.