Genome-wide association meta-analysis (GWAMA) is an effective approach to enlarge sample sizes and empower the discovery of novel associations between genotype and phenotype. Independent replication has been used as a gold-standard for validating genetic associations. However, as current GWAMA often seeks to aggregate all available datasets, it becomes impossible to find a large enough independent dataset to replicate new discoveries. Here we introduce a method, MAMBA (Meta-Analysis Model-based Assessment of replicability), for assessing the "posterior-probability-of-replicability" for identified associations by leveraging the strength and consistency of association signals between contributing studies. We demonstrate using simulations that MAMBA is more powerful and robust than existing methods, and produces more accurate genetic effects estimates. We apply MAMBA to a large-scale meta-analysis of addiction phenotypes with 1.2 million individuals. In addition to accurately identifying replicable common variant associations, MAMBA also pinpoints novel replicable rare variant associations from imputation-based GWAMA and hence greatly expands the set of analyzable variants.