The ubiquitous atmospheric dust on Mars is well mixed by periodic global dust storms, and such dust carries information about the environment in which it once formed and hence about the history of water on Mars. The Mars Exploration Rovers have permanent magnets to collect atmospheric dust for investigation by instruments on the rovers. Here we report results from Mössbauer spectroscopy and X-ray fluorescence of dust particles captured from the martian atmosphere by the magnets. The dust on the magnets contains magnetite and olivine; this indicates a basaltic origin of the dust and shows that magnetite, not maghemite, is the mineral mainly responsible for the magnetic properties of the dust. Furthermore, the dust on the magnets contains some ferric oxides, probably including nanocrystalline phases, so some alteration or oxidation of the basaltic dust seems to have occurred. The presence of olivine indicates that liquid water did not play a dominant role in the processes that formed the atmospheric dust.