The riverine export of carbon is expected to be driven by changes in connectivity between source areas and streams. Yet we lack a thorough understanding of the relative contributions of different water sources to the dissolved carbon flux, and of the way these contributions vary with seasonal changes in flow connectivity. Here we assess the temporal variations in water and associated dissolved inorganic carbon (DIC) sources and fluxes in a wet‐dry tropical river of northern Australia over two years. We use linear mixing models integrated into a Bayesian framework to determine the relative contributions of rainfall, seasonal wetlands, shallow groundwater, and a deep carbonate aquifer to riverine DIC fluxes, which we relate to the age of water sources. Our results suggest extreme shifts in water and DIC sources between the wet and dry seasons. Under wet conditions, most DIC was of biogenic origin and transported by relatively young water sources originating from shallow groundwater and wetlands. As rainfall ceased, the wetlands either dried out or became disconnected from the stream network. From this stage, DIC switched to a geogenic origin, nearly entirely conveyed via older water sources from the carbonate formation. Our findings demonstrate the importance of changing patterns of connectivity when evaluating riverine DIC export from catchments. This work also illustrates the need to systematically partition DIC fluxes between biogenic and geogenic sources, if we are to quantify how the riverine export of carbon affects net carbon soil storage.