Police will also be given new powers to seize and ground drones which may have been used in criminal activity.
The bill has been welcomed by the pilots' union, which has warned of near misses involving drones and aircraft.
In July a drone flew directly over the wing of a large passenger jet as it came into land at London's Gatwick Airport, which a report said had put 130 lives at risk.
The proposed bill - to be published in spring 2018 - would ensure that owners of drones weighing more than 250g would need to register and sit a test.
Drone pilot and trainer Elliott Corke, director of HexCam, said most recreationally and commercially-used drones in use weighed more than 250g, apart from the cheap toy versions.
He told BBC News that many new users were surprised by how many rules around drone usage already exist, under the Civil Aviation Authority's Drone Code.