We use a neural network-based estimate of the sea surface partial pressure of CO2 (pCO(2)) derived from measurements assembled within the Surface Ocean CO2 Atlas to investigate the dominant modes of pCO(2) variability from 1982 through 2015. Our analysis shows that detrended and deseasonalized sea surface pCO(2) varies substantially by region and the respective frequencies match those from the major modes of climate variability (Atlantic Multidecadal Oscillation, Pacific Decadal Oscillation, multivariate ENSO index, Southern Annular Mode), suggesting a climate modulated air-sea exchange of CO2. We find that most of the regional pCO(2) variability is driven by changes in the ocean circulation and/or changes in biology, whereas the North Atlantic variability is tightly linked to temperature variations in the surface ocean and the resulting changes in solubility. Despite the 34-year time series, our analysis reveals that we can currently only detect one to two periods of slow frequency oscillations, challenging our ability to robustly link pCO(2) variations to climate variability. Plain Language Summary In our study we show that there is a link between the amount of carbon in the surface ocean and natural climate variability. We find that this variability is very different between different oceanic regions, but most of the observed variability is on decadal timescales and longer. Current data products therefore do not extend long enough in time to robustly detect long-term oscillations of the surface ocean carbon content.