The drone could fly up to 15 miles (24 kilometers) and deliver a package within 30 minutes of the order being placed.
There was no indication of when it would be available for use by the retail giant.
The company was licensed to control delivery aircraft in the US earlier this year.
It also has centers in the United Kingdom and Israel.
The prototype will be part of a “family” of delivery aircraft, Mr Clarkson added in the clip, and is one of around a dozen devices the company is developing.
The drone is equipped with “reason and avoidance” technology and can fly at a height of 400 feet.
Safety
Lawyer Luke Scanlon, from law firm Pinsent Masons, said security could be an issue if this technology is software-based.
"The systems are based on software 'detect and avoid' and given the current climate of hacking and data breaches, it is very important that coordinated efforts are made to ensure that the systems are put in place giving the highest level of reliability in terms of security," he said.
“Once these standards are agreed upon by technical experts, the arguments for the creation of commercial drone services will gain greater support in the ongoing regulatory reform discussions and forums currently underway.”
Amazon said it would not launch the service until it was able to "prove that they are safe businesses.".
The US Federal Aviation Administration (FAA) has strict criteria for commercial drone use, and some US politicians have called for the creation of a registry of unmanned aircraft.
The FAA estimates that by 2020 there will be about 30,000 commercial drones and many more civilian devices in use in America.
