Rivers represent a significant source of greenhouse gases (GHGs), with the three main gases emitted being carbon dioxide (CO₂), methane (CH₄), and nitrous oxide (N₂O). To comprehend the spatio-temporal variability of these gases, it is essential to consider the regulating factors that influence their concentration. In larger rivers GHG concentrations are mostly regulated by in-river processes. Thus, the concentration of all these GHGs is supposed to be governed by the trophic state and the activity of phytoplankton. We performed a monthly monitoring for the three GHGs at the river Elbe (Germany) over 5 years (2020-2024); together with chlorophyll concentrations and other basic water chemical variables. CO2 concentrations showed a clear seasonal pattern with minimum values in summer, mainly driven by light availability and chlorophyll concentration (photosynthesis). CH4 concentrations showed an opposite seasonal dynamic with maximum values in summer, as indicated by its dependence on temperature and particulate organic carbon (POC). N2O concentrations were mostly near saturation and mainly determined by temperature dependent solubility. The total GHG-potential of the three gases in terms of CO2 equivalents was dominated by CO2 and its seasonal cycle. We successfully used this comprehensive dataset to develop data-driven models based on machine-learning methods, reaching coefficients of determination greater than 0.75. Looking ahead to subsequent research these models enable predictions of GHG concentrations and emissions under potential future climate scenarios.