High carbon dioxide (CO2) concentrations in sea-water (ocean hypercapnia) can induce neurological, physiological and behavioural deficiencies in marine animals. Prediction of the onset and evolution of hypercapnia in the ocean requires a good understanding of annual variations in oceanic CO2 concentration, but there is a lack of relevant global observational data. Here we identify global ocean patterns of monthly variability in carbon concentration using observations that allow us to examine the evolution of surface-ocean CO2 levels over the entire annual cycle under increasing atmospheric CO2 concentrations. We predict that the present-day amplitude of the natural oscillations in oceanic CO2 concentration will be amplified by up to tenfold in some regions by 2100, if atmospheric CO2 concentrations continue to rise throughout this century (according to the RCP8.5 scenario of the Intergovernmental Panel on Climate Change). The findings from our data are broadly consistent with projections from Earth system climate models. Our predicted amplification of the annual CO2 cycle displays distinct global patterns that may expose major fisheries in the Southern, Pacific and North Atlantic oceans to hypercapnia many decades earlier than is expected from average atmospheric CO2 concentrations. We suggest that these ocean 'CO2 hotspots' evolve as a combination of the strong seasonal dynamics of CO2 concentration and the long-term effective storage of anthropogenic CO2 in the oceans that lowers the buffer capacity in these regions, causing a nonlinear amplification of CO2 concentration over the annual cycle. The onset of ocean hypercapnia (when the partial pressure of CO2 in sea-water exceeds 1,000 micro-atmospheres) is forecast for atmospheric CO2 concentrations that exceed 650 parts per million, with hypercapnia expected in up to half the surface ocean by 2100, assuming a high-emissions scenario (RCP8.5). Such extensive ocean hypercapnia has detrimental implications for fisheries during the twenty-first century.