Insufficient understanding of the mechanism that reversibly converts sulfur into lithium sulfide (Li2S) via soluble polysulfides (PS) hampers the realization of high performance lithium-sulfur (Li-S) cells. Typically Li2S formation is explained by direct electroreduction of a PS to Li2S; however, this is not consistent with the size and shape of the insulating Li2S deposits. Here, we use operando small and wide angle X-ray scattering (SAXS/WAXS) and operando small angle neutron scattering (SANS) to track the growth and dissolution of solid deposits from atomic to sub-micron scales during charge and discharge. Stochastic modelling based on the SANS data allows quantification of the chemical phase evolution during discharge and charge. We show that the deposit is comprised of nanocrystalline Li2S and smaller, solid short-chain PS particles, which we argue are likely Li2S2. Our data are consistent with solid Li2S2 precipitating from solution and then being converted in the solid-state to Li2S, probably via direct electroreduction and chemical diffusion through the Li2S2 particle network. Solution-mediated Li2S2 precipitation, therefore, controls the Li2S/Li2S2 aggregate structure. Discharge capacity and rate capability in Li-S battery cathodes are limited by mass transport rather than electron transport through a thin passivating surface film. The found mechanism also explains why in practice not all S is converted to Li2S; a certain amount of Li2S2 remains as a second solid phase.