Reliable information about the future state of the ocean and fish stocks is necessary for informed decision-making by fisheries scientists, managers and the industry. However, multiyear regional ocean climate and fish stock predictions have until now had low forecast skill. Here, we provide skillful forecasts of the biomass of cod stocks in the North and Barents Seas a decade in advance. We develop a unified dynamical-statistical prediction system wherein statistical models link future total stock biomass to dynamical predictions of sea surface temperature, while also considering different fishing mortalities. We evaluate non-linear effects of temperature and fishing on cod biomass, and provide evidence of climate-derived predictability in cod stocks. We forecast the continuation of unfavorable oceanic conditions for the North Sea cod for the coming decade which would inhibit its recovery at present fishing levels, and a decrease in Northeast Arctic cod stock compared to the recent high levels.