Climate change is expected to impact the habitability of many places around the world in significant and unprecedented ways in the coming decades. While previous studies have provided estimates of populations potentially exposed to various climate impacts, little work has been done to assess the number of people that may actually be displaced or where they will choose to go. Here we modify a diffusion-based model of human mobility in combination with population, geographic, and climatic data to estimate the sources, destinations, and flux of potential migrants as driven by sea level rise (SLR) in Bangladesh in the years 2050 and 2100. Using only maps of population and elevation, we predict that 0.9 million people (by year 2050) to 2.1 million people (by year 2100) could be displaced by direct inundation and that almost all of this movement will occur locally within the southern half of the country. We also find that destination locations should anticipate substantial additional demands on jobs (594 000), housing (197 000), and food (783 × 109 calories) by mid-century as a result of those displaced by SLR. By linking the sources of migrants displaced by SLR with their likely destinations, we demonstrate an effective approach for predicting climate-driven migrant flows, especially in data-limited settings.