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, decadal regional ocean climate and fish stock predictions have until now had low forecast skill. Here, we provide skilful 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 stock biomass to dynamical predictions of sea surface temperature, while also considering different fishing mortalities. Our retrospective forecasts provide estimates of past performance of our models and they suggest differences in the source of prediction skill between the two cod stocks. We forecast the continuation of unfavorable oceanic conditions for the North Sea cod in 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.