We introduce the Assembly of high-ResoluTion Eagle-simulations of MIlky Way-type galaxieS (ARTEMIS) simulations, a new set of 42 zoomed-in, high-resolution (baryon particle mass of approximate to 2 x 10(4)M(circle dot) h(-1)), hydrodynamical simulations of galaxies residing in haloes of Milky Way mass, simulated with the EAGLE galaxy formation code with re-calibrated stellar feedback. In this study, we analyse the structure of stellar haloes, specifically the mass density, surface brightness, metallicity, colour, and age radial profiles, finding generally very good agreement with recent observations of local galaxies. The stellar density profiles are well fitted by broken power laws, with inner slopes of approximate to-3, outer slopes of approximate to-4, and break radii that are typically approximate to 20-40 kpc. The break radii generally mark the transition between in situ formation and accretion-driven formation of the halo. The metallicity, colour, and age profiles show mild large-scale gradients, particularly when spherically averaged or viewed along the major axes. Along the minor axes, however, the profiles are nearly flat, in agreement with observations. Overall, the structural properties can be understood by two factors: that in situ stars dominate the inner regions and that they reside in a spatially flattened distribution that is aligned with the disc. Observations targeting both the major and minor axes of galaxies are thus required to obtain a complete picture of stellar haloes.