The FAA said it had granted Amazon a certificate for people with pilot's licenses to test the unmanned aircraft.
The drones must be flown at 400 feet or below during daylight hours, and must remain within sight of the pilot.
Under US law, operating drones for commercial purposes is illegal.
However, those rules are under revision by the FAA, which is expected to issue new rules regarding the operation of unmanned aircraft for commercial and recreational purposes.Long wait
Amazon had asked the US regulator for approval to begin the tests last July.
In December, the firm warned that it might begin testing the programme - known as Amazon Prime Air - in other countries.
"Without approval of our testing in the United States, we will be forced to continue expanding our Prime Air R&D footprint abroad," wrote Paul Misener, Amazon's vice president of global public policy, in a letter to the FAA at the time.
As part of this ruling, the internet retail giant must also provide data on the number of flights conducted and any other relevant information, on a monthly basis.
Amazon announced in December 2013 that it was going to begin trialling delivery to some customers by drone.
Chinese internet giant Alibaba, Google and parcel service UPS are among other companies carrying out more private trials of drones.