The bodies of Sam Fuller, 12, and his sisters Becka, aged eight, and seven-year-old Charlotte, who was known as Charlie, were discovered yesterday morning in isolated woodland in Shropshire.
They had suffered knife wounds and their father, university graduate Ceri Fuller, 35, was also found dead in a nearby quarry.
Police said a murder investigation was launched after the finds, but they are not looking for anyone else in relation to the tragedy and said it was the result of a "tragic family situation".
Mr Fuller and his three children had left their home at Milkwall, near Coleford, Gloucester- shire, last Thursday.
Police later appealed for sightings of the four and said they were believed to have been travelled to the site near Pontesbury, Shropshire, in a red Land Rover Freelander.
Becka and Charlie were pupils at St John's Church of England Primary School in Coleford, which older brother Sam had also attended before moving to secondary school.
Headteacher Jan Wagstaff said: "Rebecca and Charlotte were absolutely delightful children and a pleasure to have in school. Sam was also a pupil here before he moved on to Lakers. He was a lot of fun and always had a ready smile. They will all be very sadly missed. Our thoughts and prayers are with their family."
Alison Elliott, head of Lakers School in Coleford, added: "We are desperately sad to hear the family are having to face such a dreadful situation.
"Sam was a well-loved member of our extended family here at Lakers. Our thoughts are with the family at this very tragic time.
"We have arrangements in place to support students, staff, friends and family at this very difficult time."
Mr Fuller married his wife Ruth in August 2009 and neighbours said they had lived in the village of Milkwall for about a year.
Neighbours said the family "kept themselves to themselves" but spoke of their shock.
Janice Ayres, who lives next door to the Fuller family, said: "Very, very sad, I just cannot say any more.
"I didn't even know her name [the children's mother]. I have children of my own and I would just be devastated."
Another neighbour, who did not wish to give their name, added: "They hadn't lived here all that long. They kept themselves to themselves."
Rachel Annis, whose daughter went to the same school as Charlotte, said: "Charlotte was in my daughter's class at St John's. She was just a beautiful little girl. They were such characters."
Mrs Fuller's father, Ron Tocknell, from Lydney, Gloucestershire, appealed for information when his son-in-law and grandchildren disappeared. He wrote on his Facebook page: "If anyone who knows Ceri has any idea of his whereabouts, please contact Glos police immediately. We are all so worried."
Mr Fuller worked as a production supervisor at the Lydney-based Glatfelter paper mill, having joined in 2002.
According to his LinkedIn profile, Mr Fuller was educated at Whitecross School in Lydney before taking A-levels in physics, chemistry, biology and general studies at the Royal Forest of Dean College. He then completed a BSc in molecular and cellular biology at the University of Huddersfield, graduating in 2001.
A spokesman for Gloucestershire Police said: "Officers searching for missing man Ceri Fuller and his three children, from the Forest of Dean, have been made aware of the discovery of four bodies in Pontesbury, Shropshire."