Paxton, who has starred in the movies Frailty, Titanic and Apollo 13, will take the role of Jeff Tracy, the retired astronaut who runs top-secret agency International Rescue.
The film version of Gerry Anderson's 1960s series is due to be filmed at Shepperton Studios later this year.
Newcomers will take the roles of four of Tracy's sons. The fifth has yet to be cast.
The Baldwin brothers - Alec, William, Steven and Daniel - had been tipped to take the roles but Star Trek actor Jonathan Frakes, who will direct the film, said the Thunderbirds rockets "would be the stars".
Philip Winchester, who had a minor part in The Patriot, will play Scott Tracy while Lex Shrapnel, a Russian crew member in K-19, will star as John.
Virgil will be played by Dominic Colenso, who starred in the BBC drama The Lost Prince, and Ben Torgenson will appear as Gordon.
The role of Lady Penelope has been taken by actress Sophia Myles, while Ron Cook will play her resourceful chauffeur, Parker.
Only the parts of Alan and the villainous Hood have yet to be filled.
Family film
The show, which was first broadcast in 1964, still has a huge following despite the fact that only 32 episodes were made.
A live-action feature based on the series has been in development for some time.
British producers Working Title and director Peter Hewitt, who made the comedy Thunderpants, have both been attached to the project over the past few years.
However, plans to turn the live-action version into an action-adventure aimed at adult audiences were recently scrapped, and the project has been rewritten as a family film aimed at the under-10s.