Amazon fought off competition from the likes of SVOD rival Netflix and UK commercial broadcaster ITV for the sought-after trio (pictured above).
Former Top Gear executive producer Andy Wilman also comes as part of the package, and will oversee a new motoring-themed show for the SVOD platform.
Clarkson, May and Hammond left the BBC after Clarkson was suspended from Top Gear when it was found he had hit a producer.
They will now front a three-season series, which is currently unnamed, that goes into production soon and launched on Amazon next year.
Clarkson has made a series of tweets about his new show, and also said, “I feel like I’ve climbed out of a bi-plane and into a spaceship” – a quip at the expense of the BBC.
Top Gear is to continue on UK pubcaster the BBC fronted by popular presenter Chris Evans, as BBC Worldwide owns rights to the name and the format, which brings in around £50 million a year.
The BBC today announced experienced entertainment producer Lisa Clark will take Wilman’s executive producer post on the show.
Jay Marine, vice-president of Amazon Prime Video in Europe, 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.
“Our approach is to give programme makers creative freedom to be innovative and make the shows they want to make. This is just the start, you should expect to see more world-leading talent and the biggest shows on Prime Video.”