In the 1950s the myxoma virus was deliberately released into wild European rabbit populations in Australia and Europe. The subsequent pandemic decimated populations and resulted in a remarkable natural experiment, where rabbits in both continents rapidly evolved resistance to the virus. We investigated the genetic basis of this resistance by comparing the exomes of modern individuals with the exomes of historical rabbit specimens collected before the virus release. By replicating our analyses in Australia, France and the United Kingdom we found a strong pattern of parallel selection across the three countries, with the same genetic variants changing in frequency over the last 60 years. Notably, these occurred in genes involved in antiviral immunity and viral replication, and support a polygenic basis of resistance. We experimentally validated the functional role of these genes as viral modulators and showed that selection acting on three amino acids in an interferon protein increased its antiviral effect.