The invention relates to a magnetic apparatus with sweepers for cleaning airport runways and to the method of use thereof. In particular, the apparatus sweeps and removes foreign object debris and waste on the surface of airport runways, such as plastic, paper, twigs, stones, and other waste. The sweepers are complementary to the magnetic apparatus for cleaning runways, forming a single, complete, homogeneous unit. The apparatus carries magnetic arms and is disposed in front of the sweepers, which are towed by the truck of the magnetic cleaning apparatus. The sweepers (2, 3) are carried on both sides of a trailer (1), and are opened by hydraulic means (15). The invention further comprises suction pipes (6, 7) originating from a main suction pipe (13), for sucking up the waste. The sweepers are large and designed for airport runways to cover a larger area of the runway in record time.