Recent advances in quantum sensors, including atomic clocks, enable searches for a broad range of dark matter candidates. The question of the dark matter distribution in the Solar system critically affects the reach of dark matter direct detection experiments. Partly motivated by the NASA Deep Space Atomic Clock (DSAC) and the Parker Solar Probe (PSP), we show that space quantum sensors present new opportunities for ultralight dark matter searches, especially for dark matter states bound to the Sun. We show that space quantum sensors can probe unexplored parameter space of ultralight dark matter, covering theoretical relaxion targets motivated by naturalness and Higgs mixing. If an atomic clock were able to make measurements on the interior of the solar system, it could probe this highly sensitive region directly and set very strong constraints on the existence of such a bound-state halo in our solar system. We present sensitivity projections for space-based probes of ultralight dark matter which couples to electron, photon, and gluon fields, based on current and future atomic, molecular, and nuclear clocks.