A producer and writer, Ms Anderson created the Supermarionation puppet series with husband Gerry.
She died at her home in Bray, Berkshire, following a short illness, her daughter Dee Anderson confirmed.
"Sylvia was a mother and a legend - her intelligence was phenomenal but her creativity and tenacity unchallenged," her daughter said.
"She was a force in every way, and will be sadly missed."
Gerry Anderson died in 2012 aged 83 after suffering with Alzheimer's disease.
As well as voicing Lady Penelope Creighton-Ward in Thunderbirds from its debut in 1965 until 1968, Sylvia also worked on Joe 90, Captain Scarlet and Stingray.
Born in south London to a boxing champion and a dressmaker, she went on to have a career in television spanning five decades.
She recently worked as head of programming for HBO in the UK and had been writing a show with her daughter entitled The Last Station.
Ms Anderson said her mother "would always find time to take care of people who were suffering or in need of support".
The pair had planned a charity ball for Breast Cancer Care, which will now go ahead in May in her memory.
She is survived by her daughter, who is a singer-songwriter, son Gerry Anderson Junior, an anaesthetist, four grandchildren and one great-granddaughter.
Speaking last September, Mrs Anderson said she had had "fun" playing a great aunt to her original character, voiced by Oscar nominee Rosamund Pike, in ITV reboot Thunderbirds Are Go.
She had a "creativity and genuine love for her characters" that touched fans around the world, her daughter said.
Behind the camera, she took on many roles for Thunderbirds, including character development and costume design.
When asked if she saw herself as a pioneer for women in television during the 1960s, Mrs Anderson was modest.
"I never waved the flag or anything about being a woman, but I was a woman with a group of men. Now and again I would get a director and I would go on set, one in particular, no names of course, and he was very, very huffy because I was a woman giving him notes on what he had shot the previous day, and I tried to do it very carefully," she said.