Genomic data analysis across multiple cloud platforms is an ongoing challenge, especially when large amounts of data are involved. Here, we present Swarm, a framework for federated computation that promotes minimal data motion and facilitates crosstalk between genomic datasets stored on various cloud platforms. We demonstrate its utility via common inquiries of genomic variants across BigQuery in the Google Cloud Platform (GCP), Athena in the Amazon Web Services (AWS), Apache Presto and MySQL. Compared to single-cloud platforms, the Swarm framework significantly reduced computational costs, run-time delays and risks of security breach and privacy violation.