Heterogeneous ice nucleation is a ubiquitous process in the natural and built environment. Deposition ice nucleation, i.e. heterogeneous ice nucleation that - according to the traditional view - occurs in a subsaturated water vapor environment and in the absence of supercooled water on the solid, ice-forming surface, is among the most important ice formation processes in high-altitude cirrus and mixed-phase clouds. Despite its importance, very little is known about the mechanism of deposition ice nucleation at the microscopic level. This study puts forward an adsorption-based mechanism for deposition ice nucleation through results from a combination of atomistic simulations, experiments and theoretical modelling. One of the most potent laboratory surrogates of ice nucleating particles, silver iodide, is used as a substrate for the simulations. We find that water initially adsorbs in clusters which merge and grow over time to form layers of supercooled water. Ice nucleation on silver iodide requires at minimum the adsorption of 4 molecular layers of water. Guided by the simulations we propose the following fundamental freezing steps: (1) Water molecules adsorb on the surface, forming nanodroplets. (2) The supercooled water nanodroplets merge into a continuous multilayer when they grow to about 3 molecular layers thick. (3) The layer continues to grow until the critical thickness for freezing is reached. (4) The critical ice cluster continues to grow.|Schematic of the proposed deposition ice nucleation mechanism on AgI (0001).