Sea-level rise and ensuing permanent coastal inundation will cause spatial shifts in population and economic activity over the next 200 years. Using a highly spatially disaggregated, dynamic model of the world economy that accounts for the dynamics of migration, trade, and innovation, this paper estimates the consequences of probabilistic projections of local sea-level changes under different emissions scenarios. Under an intermediate greenhouse gas concentration trajectory, permanent flooding is projected to reduce global real GDP by an average of 0.19% in present value terms, with welfare declining by 0.24% as people move to places with less attractive amenities. By the year 2200 a projected 1.46% of world population will be displaced. Losses in many coastal localities are more than an order of magnitude larger, with some low-lying urban areas particularly hard hit. When ignoring the dynamic economic adaptation of investment and migration to flooding, the loss in real GDP in 2200 increases from 0.11% to 4.5%. This shows the importance of including dynamic adaptation in future loss models.