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Many important biological functions arise not from single genes, but from complex interactions encoded by entire genomes. Genome language models have emerged as a promising strategy for designing biological systems, but their ability to generate functional sequences at the scale of whole genomes has remained untested. Here, we report the first generative design of viable bacteriophage genomes. We leveraged frontier genome language models, Evo 1 and Evo 2, to generate whole-genome sequences with realistic genetic architectures and desirable host tropism, using the lytic phage ΦX174 as our design template. Experimental testing of AI-generated genomes yielded 16 viable phages with substantial evolutionary novelty. Cryo-electron microscopy revealed that one of the generated phages utilizes an evolutionarily distant DNA packaging protein within its capsid. Multiple phages demonstrate higher fitness than ΦX174 in growth competitions and in their lysis kinetics. A cocktail of the generated phages rapidly overcomes ΦX174-resistance in three E. coli strains, demonstrating the potential utility of our approach for designing phage therapies against rapidly evolving bacterial pathogens. This work provides a blueprint for the design of diverse synthetic bacteriophages and, more broadly, lays a foundation for the generative design of useful living systems at the genome scale.