The trio will create a Top Gear-style motoring show for Amazon's Prime Video service, with long-time collaborator and the show's executive producer Andy Wilman.
The new series's first episodes will premiere late this year but will be only be available to members of the £79-a-year Prime subscription service, after Amazon beat off stiff competition to win the global rights to their new show.
"I feel like I've climbed out of a bi-plane and into a spaceship", said Clarkson of making the switch from a traditional broadcaster to Amazon.
Speculation has surrounded the next step of the former Top Gear presenters since May and Hammond followed Clarkson out of the BBC when he was sacked for assaulting a producer on the popular show.
Top Gear has a global audience of 350m according to the BBC, who have picked presenter Chris Evans to replace Clarkson as the face of the show.
Its value to the broadcaster was demonstrated by the 5m fall in viewers suffered by BBC2 the Sunday after it was taken off the air.
“Customers told us they wanted to see the team back on screen, and we are excited to make that happen,” said Jay Marine, vice president of Amazon Prime Video EU.
“Millions of Prime members are already enjoying our ground-breaking original shows. We can’t wait to see what Jeremy, Richard, James and the team will create in what is sure to be one of the most globally anticipated shows of 2016."
Clarkson's new show marks a further push into creating original programming for its online video service, which boasts the largest selection of any streaming service in the UK.
"Our approach is to give programme makers creative freedom to be innovative and make the shows they want to make," said Marine. "This is just the start, you should expect to see more world-leading talent and the biggest shows on Prime Video.”