Large-scale currents in the ionosphere are driven by a variety of sources, including neutral winds, gravity, and plasma pressure gradients. While the stronger daytime wind-driven currents have been extensively studied, gravity and diamagnetic currents in the ionosphere have received very little attention but can have substantial effects even during the night. With the availability of a new generation of magnetic field models based on high-accuracy satellite magnetic measurements, it becomes increasingly important to account for these smaller current systems. In this work, we use the stand-alone NCAR TIEGCM electrodynamics solver along with empirical density, wind, and temperature inputs to model the global current systems caused by gravity and diamagnetism in the F region ionosphere and calculate their magnetic perturbations. These results allow us for the first time to visualize the global structure of these currents and quantify their magnetic perturbations. We find a significantly higher gravity-driven current during the night than one would expect from the lower conductivity which is primarily due to a Pedersen current driven by polarization charges in the predawn sector. We find some discrepancies between the diamagnetic perturbation and a theoretical prediction which could be a result of magnetic tension due to the curvature of the geomagnetic field lines. These results will allow geomagnetic field modelers to account for these important current systems and create more accurate models. This work will also be crucial in analyzing ionospheric magnetic field measurements from upcoming satellite missions such as Swarm.