Ocean microbes drive biogeochemical cycling on a global scale. However, this cycling is constrained by viruses that affect community composition, metabolic activity, and evolutionary trajectories. Owing to challenges with the sampling and cultivation of viruses, genome-level viral diversity remains poorly described and grossly understudied, with less than 1% of observed surface-ocean viruses known. Here we assemble complete genomes and large genomic fragments from both surface- and deep-ocean viruses sampled during the Tara Oceans and Malaspina research expeditions, and analyse the resulting 'global ocean virome' dataset to present a global map of abundant, double-stranded DNA viruses complete with genomic and ecological contexts. A total of 15,222 epipelagic and mesopelagic viral populations were identified, comprising 867 viral clusters (defined as approximately genus-level groups). This roughly triples the number of known ocean viral populations and doubles the number of candidate bacterial and archaeal virus genera, providing a near-complete sampling of epipelagic communities at both the population and viral-cluster level. We found that 38 of the 867 viral clusters were locally or globally abundant, together accounting for nearly half of the viral populations in any global ocean virome sample. While two-thirds of these clusters represent newly described viruses lacking any cultivated representative, most could be computationally linked to dominant, ecologically relevant microbial hosts. Moreover, we identified 243 viral-encoded auxiliary metabolic genes, of which only 95 were previously known. Deeper analyses of four of these auxiliary metabolic genes (dsrC, soxYZ, P-II (also known as glnB) and amoC) revealed that abundant viruses may directly manipulate sulfur and nitrogen cycling throughout the epipelagic ocean. This viral catalog and functional analyses provide a necessary foundation for the meaningful integration of viruses into ecosystem models where they act as key players in nutrient cycling and trophic networks.