Anticipating the effect of climate change on biodiversity, in particular on changes in community composition, is crucial for adaptive ecosystem management1 but remains a critical knowledge gap2. Here, we use climate velocity trajectories3, together with information on thermal tolerances and habitat preferences, to project changes in global patterns of marine species richness and community composition under IPCC Representative Concentration Pathways4 (RCPs) 4.5 and 8.5. Our simple, intuitive approach emphasizes climate connectivity, and enables us to model over 12 times as many species as previous studies5, 6. We find that range expansions prevail over contractions for both RCPs up to 2100, producing a net local increase in richness globally, and temporal changes in composition, driven by the redistribution rather than the loss of diversity. Conversely, widespread invasions homogenize present-day communities across multiple regions. High extirpation rates are expected regionally (for example, Indo-Pacific), particularly under RCP8.5, leading to strong decreases in richness and the anticipated formation of no-analogue communities where invasions are common. The spatial congruence of these patterns with contemporary human impacts7, 8 highlights potential areas of future conservation concern. These results strongly suggest that the millennial stability of current global marine diversity patterns, against which conservation plans are assessed, will change rapidly over the course of the century in response to ocean warming.