The parents of a five-year-old boy who had died from natural causes jumped to their deaths from Beachy Head with his body in a rucksack, it is believed.
Rescuers, who are not treating the deaths as suspicious, found a second rucksack nearby full of toys.
Chief Insp Dick Coates said police knew the identities of the family, who are not believed to be from Sussex, but had not yet talked to their next of kin.
"Later today we will be able to clarify the circumstances fully," he said.
"But I need to do what is right with the relatives first."
A silver Volkswagen camper van was recovered from a roadside car park about 200 yards (183m) from the cliff edge and taken to Eastbourne for forensic examination.
Police and coastguards used special equipment to retrieve the bodies
Coastguards on routine patrol first spotted what they thought were two bodies 400ft (120m) down the cliff face on Sunday evening.
The two rucksacks were discovered on Monday and the bodies recovered by 1400 BST.
Ch Insp Coates said it had been very traumatic for the emergency services.
"Having to recover bodies from the bottom of the cliffs is always a traumatic ordeal," he said.
"But with a child being involved it does make it a lot more sensitive for the people who are doing it."
The cliffs at Beachy Head reach up to about 600ft (180m) high and are a notorious suicide spot.
According to Eastbourne Coastguard station officer Stuart McNab, about 20 people jump to their deaths from the cliffs at Beachy Head every year.
A chaplaincy team was set up in 2004 to try to prevent suicides.
"The chaplaincy service, the coastguards and ourselves patrol that area as much as possible," said Chief Insp Coates.
"The danger of the cliffs is very well signposted by the local council."