Accurate and comprehensive measurements of economic well-being are fundamental inputs into both research and policy, but such measures are unavailable at a local level in many parts of the world. Here we train deep learning models to predict survey-based estimates of asset wealth across ~ 20,000 African villages from publicly-available multispectral satellite imagery. Models can explain 70% of the variation in ground-measured village wealth in countries where the model was not trained, outperforming previous benchmarks from high-resolution imagery, and comparison with independent wealth measurements from censuses suggests that errors in satellite estimates are comparable to errors in existing ground data. Satellite-based estimates can also explain up to 50% of the variation in district-aggregated changes in wealth over time, with daytime imagery particularly useful in this task. We demonstrate the utility of satellite-based estimates for research and policy, and demonstrate their scalability by creating a wealth map for Africa's most populous country.