Neil Puttick, 34, from Westbury in Wiltshire, died alongside his Japanese wife Kazumi, 44.
Their son was named as Samuel Puttick, aged five, who had died a day earlier from meningitis.
Samuel Puttick had been discharged from hospital on Friday after being given no hope of survival.
Samuel’s body was found on Monday in a rucksack about 120 metres (400ft) down the notorious suicide spot, near Eastbourne, East Sussex, alongside his parents’ bodies.
Detective Inspector Ian Williams from Sussex Police said: “As a result of our investigation I am satisfied that Samuel’s grieving parents Neil and Kazumi appear to have taken their own lives.
“This is a tragic incident and we extend our sympathies to their family.”