Abstract Understanding and engineering exciton transport in quantum dot (QD) solids is both of fundamental interest and crucial to their broad applications in devices1-6. Till date, studies of exciton transport in QD solids on pico/nano-second timescales have led to the conclusion that closer packing of QDs enables faster exciton transport, while energetic/structural heterogeneity leads to reduction of exciton diffusivity over time7,8. Here we study PbS QD solids using transient absorption microscopy with 13 femtoseconds time resolution and 10 nm spatial precision. We find exciton diffusivities in the range of ~102 cm2 s-1 within the first few hundred femtoseconds after photoexcitation, followed by the transition to a slower transport regime with diffusivities in the range 10-1 to 1 cm2 s-1. Counterintuitively, the initial diffusivity is higher and the time before the transition to the slower transport phase is longer in QD solids with longer ligand lengths. This suggests a transition from early-time transport of delocalized excitons to later time hopping based transport of localized excitons, where QD packing density and heterogeneity accelerate the localization process. Our results reveal a new regime for exciton transport in QD solids and provide design rules to engineer desired transport properties in these systems on a range of timescales.