Amazon's agreement with the CAA grants it a series of concessions on drone flying rules. Amazon will be able to operate its vehicles without a direct line of sight, and will be able to trial "sense and avoid" technology that lets the drones automatically evade obstacles in the air.
Unlike other drone flights, which require a pilot to be in control of a drone all times, Amazon will also be able to allow one pilot to control multiple autonomous vehicles. The restrictions are only being lifted in certain "controlled spaces" approved by the CAA.
Amazon unveiled the second prototype of its Prime Air drone last year. The vehicle, which is able to take off and land vertically but fly like a plane to cover distances, can fly for 10 miles at an altitude of 400 feet and carry packages of up to 5lb, but much of its autonomous flying technology is yet to be fully tested.
When Mr Bezos announced the drone programme in 2013, he suggested that it could be available within four or five years, although the company does not have a firm date.
Paul Misener, Amazon's vice president of global innovation policy and communications, said the UK "had been a world leader in enabling drone innovation".
"This announcement strengthens our partnership with the UK and brings Amazon closer to our goal of using drones to safely deliver parcels in 30 minutes to customers in the UK and elsewhere around the world," he said.
"We want to enable the innovation that arises from the development of drone technology by safely integrating drones into the overall aviation system," said Tim Johnson, the CAA's head of policy. "These tests by Amazon will help inform our policy and future approach."