Plant-associated microorganisms are essential for their hosts' survival and performance. Yet, most plant microbiome studies to date have focused on terrestrial species sampled across relatively small spatial scales. Here we report results of a global-scale analysis of microbial communities associated with leaf and root surfaces of the marine eelgrass Zostera marina throughout its range in the Northern Hemisphere. By contrasting host microbiomes with those of their surrounding seawater and sediment communities, we uncovered the structure, composition and variability of microbial communities associated with Z. marina. We also investigated hypotheses about the mechanisms driving assembly of the eelgrass microbiome using a whole-genomic metabolic modeling approach. Our results reveal aboveground leaf communities displaying high variability and spatial turnover, that strongly mirror their adjacent coastal seawater microbiomes. In contrast, roots showed relatively low spatial turnover and were compositionally distinct from surrounding sediment communities - a result driven by the enrichment of predicted sulfur-oxidizing bacterial taxa on root surfaces. Metabolic modeling of enriched taxa was consistent with an assembly process whereby similarity in resource use drives taxonomic co-occurrence patterns on belowground, but not aboveground, host tissues. Our work provides evidence for a core Z. marina root microbiome with putative functional roles and highlights potentially disparate processes influencing microbiome assembly on different plant compartments.