The show - hosted by Davina McCall and Alex Brooker - will see 12 celebrities competing against each other in six winter sports.
Five time Olympian Redgrave will be joined by cricketer Darren Gough, comedian Marcus Brigstocke, hairdresser Nicky Clarke, socialite Henry Conway and Flash Gordon star Sam Jones.
Meanwhile, Sinitta and Childs will be joined by four other female competitors - Tara Palmer-Tomkinson, Pussycat Doll Kimberly Wyatt, Anthea Turner and Melinda Messenger.
The 12 famous faces will be trained by Olympic skier Graham Bell and Olympic skeleton star Amy Williams, as they take part in Skeleton, Bobsleigh, Speed Skating, Skier Cross and Slalom.
Legendary Olympian Eddie 'The Eagle' Edwards will also coach the stars, and suggested that the competition is about "mental strength" as much as "physical agility".
"Winter sports are tough to master. It takes skill, guts and determination to get round a course," said Edwards. "The ultimate test will be The Jump itself. I know how hard it can be when the world is watching."
Each night, two celebrities will face a live Ski Jump to keep their place in the competition.
"Skiing is tough enough to learn as it is, so what these guys are taking on is really impressive," McCall said. "It's shaping up to be butt-clenchingly exciting!"
The Jump will air on Channel 4 for ten nights early next year.
Catch up on all the latest TV and Movies releases in Digital Spy's Screen Time: