The trio will front three series of a new motoring programme for Amazon Prime, with the first season to be made available worldwide next year.
The move follows their departure from the hit BBC Two show earlier this year.
Clarkson's contract was not renewed following an "unprovoked physical attack" on a Top Gear producer.
His co-hosts then followed him in leaving the show.
Amazon Prime Video EU vice president Jay Marine said: "Customers told us they wanted to see the team back on screen, and we are excited to make that happen.
"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."
