Ceri Fuller, 35, is thought to have stabbed his 12-year-old son Sam and daughters Rebecca, eight, and Charlotte, seven, before falling to his death from an 80ft cliff in what police described as a "tragic family situation".
All four bodies of the dead were found at the bottom of a disused quarry and may have lain there for days.
Police said Mr Fuller's red Land Rover Freelander had been parked since last Thursday at the entrance to the woodland in Pontesbury, near Shrewsbury, 300 yards from where the discovery was made.
Detective Chief Inspector Neil Jamieson said the four bodies were found "within 30 or 40 yards of each other".
He added: "A murder investigation has begun into the deaths of these individuals and a team of detectives and forensic experts are currently investigating the circumstances surrounding these deaths.
"At this stage we are not looking for anyone else in connection with this incident," he said. "Although the investigation is in its early stages, it appears to be a tragic family situation."
