The trio have committed to three seasons with the Amazon after leaving the hit BBC show after Clarkson was dropped following a fracas with a member of the production staff.
The new show, which will be produced by their long-time executive producer Andy Wilman, will be available exclusively to Amazon Prime customers next year around the world and will go into production “soon”.
Hammond added: “Amazon? Oh yes. I have already been there. I got bitten by a bullet ant.”
May said: “We have become part of the new age of smart TV. Ironic, isn’t it?”
He wrote: “I’m very excited to announce that Hammond, May and I have signed a deal with .@AmazonVideo”
Hammond also joked that he would need to “practice driving again” before filming starts.
“Haircut, clean jeans and practice driving again. Forrrrwaaaaaaaard!!
May jokingly tweeted: “Good news! I’ve got a job with @AmazonVideoUK. Bad news! So have the other two. #AmazonPrime #ItSaysHere”
Jay Marine, Vice President of Amazon Prime Video EU, said: “Customers told us they wanted to see the team back on screen, and we are excited to make that happen.
“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.”
He tweeted: “I’ve got a job I’ve got a job I’ve got a job.Clarkson also took to Twitter to admit he was “very excited” about the deal.Clarkson said: “I feel like I’ve climbed out of a bi-plane and into a spaceship.”