Human activities are changing habitats and climates and causing species’ ranges to shift. Range expansion brings into play a set of powerful evolutionary forces at the expanding range edge that act to increase dispersal rates. One likely consequence of these forces is accelerating rates of range advance because of evolved increases in dispersal on the range edge. In northern Australia, cane toads have increased their rate of spread fivefold in the last 70 years. Our breeding trials with toads from populations spanning the species’ invasion history in Australia suggest a genetic basis to dispersal rates and interpopulation genetic variation in such rates. Toads whose parents were from the expanding range front dispersed faster than toads whose parents were from the core of the range. This difference reflects patterns found in their field-collected mothers and fathers and points to heritable variance in the traits that have accelerated the toads’ rate of invasion across tropical Australia over recent decades. Taken together with demonstrated spatial assortment by dispersal ability occurring on the expanding front, these results point firmly to ongoing evolution as a driving force in the accelerated expansion of toads across northern Australia.