The ongoing uptake of anthropogenic carbon by the ocean leads to ocean acidification, a process that results in a reduction in pH and in the saturation state of biogenic calcium carbonate minerals aragonite (Omega(arag)) and calcite (Omega(calc))(1,2). Because of its naturally low Omega(arag) and Omega(calc) (refs. (2,3)), the Arctic Ocean is considered the region most susceptible to future acidification and associated ecosystem impacts(4-7). However, the magnitude of projected twenty-first century acidification differs strongly across Earth system models(8). Here we identify an emergent multi-model relationship between the simulated present-day density of Arctic Ocean surface waters, used as a proxy for Arctic deep-water formation, and projections of the anthropogenic carbon inventory and coincident acidification. By applying observations of sea surface density, we constrain the end of twenty-first century Arctic Ocean anthropogenic carbon inventory to 9.0 +/- 1.6 petagrams of carbon and the basin-averaged Omega(arag) and Omega(calc) to 0.76 +/- 0.06 and 1.19 +/- 0.09, respectively, under the high-emissions Representative Concentration Pathway 8.5 climate scenario. Our results indicate greater regional anthropogenic carbon storage and ocean acidification than previously projected3,8 and increase the probability that large parts of the mesopelagic Arctic Ocean will be undersaturated with respect to calcite by the end of the century. This increased rate of Arctic Ocean acidification, combined with rapidly changing physical and biogeochemical Arctic conditions(9-11), is likely to exacerbate the impact of climate change on vulnerable Arctic marine ecosystems.