The time of arrival of people in Australia is an unresolved question. It is relevant to debates about when modern humans first dispersed out of Africa and when their descendants incorporated genetic material from Neanderthals, Denisovans and possibly other hominins. Humans have also been implicated in the extinction of Australia's megafauna. Here we report the results of new excavations conducted at Madjedbebe, a rock shelter in northern Australia. Artefacts in primary depositional context are concentrated in three dense bands, with the stratigraphic integrity of the deposit demonstrated by artefact refits and by optical dating and other analyses of the sediments. Human occupation began around 65,000 years ago, with a distinctive stone tool assemblage including grinding stones, ground ochres, reflective additives and ground-edge hatchet heads. This evidence sets a new minimum age for the arrival of humans in Australia, the dispersal of modern humans out of Africa, and the subsequent interactions of modern humans with Neanderthals and Denisovans.