Currents are unique drivers of oceanic phylogeography and so determine the distribution of marine coastal species, along with past glaciations and sea level changes. Here, we reconstruct the worldwide colonization history of eelgrass (Zostera marina L.), the most widely distributed marine flowering plant or seagrass from its origin in the Northwest Pacific, based on nuclear and chloroplast genomes. We identified two divergent Pacific clades with evidence for admixture along the East Pacific coast. Multiple west to east (trans-Pacific) colonization events support the key role of the North Pacific Current. Time-calibrated nuclear and chloroplast phylogenies yielded concordant estimates of the arrival of Z. marina in the Atlantic through the Canadian Arctic, suggesting that eelgrass-based ecosystems, hotspots of biodiversity and carbon sequestration, have only been present since ~208 Kya (thousand years ago). Mediterranean populations were founded ~53 Kya while extant distributions along western and eastern Atlantic shores coincide with the end of the Last Glacial Maximum (~20 Kya). The recent colonization and 5- to 7-fold lower genomic diversity of Atlantic compared to the Pacific populations raises concern and opportunity about how Atlantic eelgrass might respond to rapidly warming coastal oceans.