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Sharing data across institutions for genome-wide association studies (GWAS) would enhance the discovery of genetic variation linked to health and disease. However, existing data-sharing regulations limit the scope of such collaborations. Although cryptographic tools for secure computation promise to enable collaborative analysis with formal privacy guarantees, existing approaches either are computationally impractical or do not implement current state-of-the-art methods. We introduce secure federated genome-wide association studies (SF-GWAS), a combination of secure computation frameworks and distributed algorithms that empowers efficient and accurate GWAS on private data held by multiple entities while ensuring data confidentiality. SF-GWAS supports widely used GWAS pipelines based on principal-component analysis or linear mixed models. We demonstrate the accuracy and practical runtimes of SF-GWAS on five datasets, including a UK Biobank cohort of 410,000 individuals, showcasing an order-of-magnitude improvement in runtime compared to previous methods. Our work enables secure collaborative genomic studies at unprecedented scale.