Two children are thought to have been stabbed by their father before he took his own life, the BBC understands.
Police believe the man was Michael Pedersen, from Surrey, who was found in Newton Stacey, Hampshire, with his children Ben, seven, and Freya, six.
It is thought Mr Pedersen, 51, who was estranged from the children's mother, was visiting his father in Andover.
The children had already been found dead before their mother reported them missing on Sunday evening, police said.
Det Supt Tony Harris, of Hampshire Police, said the "tragic incident" happened during an arranged visit.
He said Surrey Police was considering referring the case to the Independent Police Complaints Commission (IPCC) because of some previous contact with Mr Pedersen.
'Extremely distressing'
Surrey County Council said it could not yet comment on whether Mr Pedersen was known to social services as there has been no formal identification.
The 51-year-old was also thought to be a former serviceman although the Ministry of Defence would not give further details.
He was living in Chertsey, Surrey, while his children were living with their mother Erica in Ashford, Surrey, and attended Ashford Primary School.
Head teacher Caroline Dyer said: "We are all deeply shocked and saddened at this news.
"The school is in contact with the relevant authorities but as this is currently the subject of a police investigation we are unable to make any further comment."
The children's maternal grandfather, William Clifford, 67, said outside his daughter's home: "We are obviously devastated and what we would ask is that you respect our privacy in this matter."
The three bodies were found next to a car by a dog walker at about 18:15 BST.
Post-mortem examinations are due to be carried out later.
Newton Stacey is about five miles south of Andover, between Chilbolton and Barton Stacey, and is made up of a handful of cottages and country homes.
'Terrible incident'
Passer-by Andy Harris, who lives locally, was in the area with his wife.
He said: "It's shocking, you don't know what to think. You don't expect this type of thing in the countryside."
Det Supt Tony Harris, of Hampshire Constabulary, said: "Throughout the night, police worked to identify the families of the victims and notify them of what had been discovered.
"A Home Office pathologist attended the scene and at this stage it appears that the children suffered fatal stab wounds and Mr Pedersen took his own life soon afterwards.
"We are treating this as an isolated incident and we do not believe anyone else was involved.
"The families of Michael, Ben and Freya have been informed and specialist family liaison officers from Hampshire Constabulary and officers from Surrey Police are working with them to provide support and keep them updated as the investigation progresses.
"Our thoughts are with the family and friends of those involved at this extremely difficult time and I would ask that they be allowed to come to terms with what has happened in a dignified and respectful way."
Police said the coroner had been informed.
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