We report the discovery of the Oceanus moving group, a ~500Myr old group with 50 members and candidate members at distances 2-50pc from the Sun, using an unsupervised clustering analysis of nearby stars with Gaia DR3 data. This new moving group includes the nearest brown dwarf WISE J104915.57-531906.1 AB (Luhman 16 AB) at a distance of 2pc, which was previously suspected to be young (600-800Myr) based on a comparison of its dynamical mass measurements with brown dwarf evolutionary models. We use empirical color-magnitude sequences, stellar activity, and gyrochronology to determine that this new group is roughly coeval with the Coma Ber open cluster, with an isochronal age of 510+/-95Myr. This newly discovered group will be useful to refine the age and chemical composition of Luhman 16 AB, which is already one of the best substellar benchmarks known to date. Furthermore, the Oceanus moving group is one of the nearest young moving groups identified to date, making it a valuable laboratory for the study of exoplanets and substellar members, with eight brown dwarf candidate members already identified here.