Polygenic Risk Scores (PRS) have huge potential to contribute to biomedical research and to a future of precision medicine, but to date their calculation relies largely on Europeanancestry GWAS data. This global bias makes most PRS substantially less accurate in individuals of non-European ancestry. Here we present BridgePRS , a novel Bayesian PRS method that leverages shared genetic effects across ancestries to increase the accuracy of PRS in non-European populations. The performance of BridgePRS is evaluated in simulated data and real UK Biobank (UKB) data across 19 traits in African, South Asian and East Asian ancestry individuals, using both UKB and Biobank Japan GWAS summary statistics. BridgePRS is compared to the leading alternative, PRS-CSx , and two single-ancestry PRS methods adapted for trans-ancestry prediction. PRS trained in the UK Biobank are then validated out-of-cohort in the independent Mount Sinai (New York) Bio Me Biobank. Simulations reveal that BridgePRS performance, relative to PRS-CSx , increases as uncertainty increases: with lower heritability, higher polygenicity, greater between-population genetic diversity, and when causal variants are not present in the data. Our simulation results are consistent with real data analyses in which BridgePRS has better predictive accuracy in African ancestry samples, especially in out-of-cohort prediction (into Bio Me ), which shows a 60% boost in mean R 2 compared to PRS-CSx ( P = 2 × 10 -6 ). BridgePRS performs the full PRS analysis pipeline, is computationally efficient, and is a powerful method for deriving PRS in diverse and under-represented ancestry populations.