Lateral transfer of carbon (C) from terrestrial ecosystems into the inland water network is an important component of the global C cycle, which sustains a large aquatic CO2 evasion flux fuelled by the decomposition of allochthonous C inputs. Globally, estimates of the total C exports through the terrestrial–aquatic interface range from 1.5 to 2.7 Pg C yr−1 (Cole et al., 2007; Battin et al., 2009; Tranvik et al., 2009), i.e. of the order of 2–5 % of the terrestrial NPP. Earth system models (ESMs) of the climate system ignore these lateral transfers of C, and thus likely overestimate the terrestrial C sink. In this study, we present the implementation of fluvial transport of dissolved organic carbon (DOC) and CO2 into ORCHIDEE (Organising Carbon and Hydrology in Dynamic Ecosystems), the land surface scheme of the Institut Pierre-Simon Laplace ESM. This new model branch, called ORCHILEAK, represents DOC production from canopy and soils, DOC and CO2 leaching from soils to streams, DOC decomposition, and CO2 evasion to the atmosphere during its lateral transport in rivers, as well as exchange with the soil carbon and litter stocks on floodplains and in swamps. We parameterized and validated ORCHILEAK for the Amazon basin, the world's largest river system with regard to discharge and one of the most productive ecosystems in the world. With ORCHILEAK, we are able to reproduce observed terrestrial and aquatic fluxes of DOC and CO2 in the Amazon basin, both in terms of mean values and seasonality. In addition, we are able to resolve the spatio-temporal variability in C fluxes along the canopy–soil–water continuum at high resolution (1°, daily) and to quantify the different terrestrial contributions to the aquatic C fluxes. We simulate that more than two-thirds of the Amazon's fluvial DOC export are contributed by the decomposition of submerged litter. Throughfall DOC fluxes from canopy to ground are about as high as the total DOC inputs to inland waters. The latter, however, are mainly sustained by litter decomposition. Decomposition of DOC and submerged plant litter contributes slightly more than half of the CO2 evasion from the water surface, while the remainder is contributed by soil respiration. Total CO2 evasion from the water surface equals about 5 % of the terrestrial NPP. Our results highlight that ORCHILEAK is well suited to simulate carbon transfers along the terrestrial–aquatic continuum of tropical forests. It also opens the perspective that provided parameterization, calibration and validation is performed for other biomes, the new model branch could improve the quantification of the global terrestrial C sink and help better constrain carbon cycle–climate feedbacks in future projections.