The origin of micrometeorites (MMs) from asteroids and comets is well-established, but the relative contribution from these two classes remains poorly resolved. Likewise, determining the precise origin of individual MMs is an open challenge. Here, cosmic-ray exposure ages are used to resolve the spatial origins of 12 MMs collected from urban areas and Antarctica. Their Al-26 and Be-10 concentration, produced during cosmic-ray irradiation in space, were measured by accelerator mass spectrometry. These data are compared to results from a model simulating the transport and irradiation of the MM precursors in space. This model, for the first time, considers a variety of orbits, precursor particle sizes, compositions and densities and incorporates non-isotropic solar and galactic cosmic-ray flux profiles, depth-dependent production rates, as well as spherical evaporation during atmospheric entry. While the origin for six MMs remains ambiguous, two MMs show a preferential tendency towards an origin in the Inner Solar System (Near Earth Objects to the Asteroid Belt) and four towards an origin in the Outer Solar System (Jupiter Family Comets to the Kuiper Belt). These findings challenge the notion that dust originating from the Outer Solar System is unlikely to survive long-term transport and delivery to the terrestrial planets. This article is part of the theme issue 'Dust in the Solar System and beyond'.