Cs2AgF4 was proposed to be an orbitally ordered ferromagnet based on recent neutron scattering data. Here, we report a detailed electronic structure study within the local spin density approximation also including strong Coulomb repulsion U. We investigate the influence of an orthorhombic distortion of the Ag environment and the importance of the on-site Coulomb repulsion. We find good quantitative agreement with both the experimentally observed exchange coupling and structural changes. Thus, our results strongly support that Cs2AgF4 is a strongly correlated charge-transfer insulator where the ferromagnetism is driven by orbital order.