Anderson had been suffering from Alzheimer's Disease since 2010 and his health had deteriorated in the past six months, Jamie Anderson said on his personal website.
The animator also created "Joe 90" and "Stingray", but he was best known for "Thunderbirds", which used a form of marionette puppetry dubbed "Supermarionation"
The series, first shown in 1965, followed the adventures of International Rescue, a secretive organisation whose mission was to help those in peril using spacecraft and a range of vehicles.
His son said: "I'm very sad to announce the death of my father, Thunderbirds creator, Gerry Anderson.
"He died peacefully in his sleep at midday today having suffered with mixed dementia for the past few years."