The attenuation of myxoma virus (MYXV) following its introduction as a biological control into the European rabbit populations of Australia and Europe is the canonical study of the evolution of virulence. However, the evolutionary genetics of this profound change in host-pathogen relationship is unknown. We describe the genome-scale evolution of MYXV covering a range of virulence grades sampled over 49 years from the parallel Australian and European epidemics, including the high-virulence progenitor strains released in the early 1950s. MYXV evolved rapidly over the sampling period, exhibiting one of the highest nucleotide substitution rates ever reported for a double-stranded DNA virus, and indicative of a relatively high mutation rate and/or a continually changing selective environment. Our comparative sequence data reveal that changes in virulence involved multiple genes, likely losses of gene function due to insertion-deletion events, and no mutations common to specific virulence grades. Hence, despite the similarity in selection pressures there are multiple genetic routes to attain either highly virulent or attenuated phenotypes in MYXV, resulting in convergence for phenotype but not genotype.