Abstract The origin of our Galaxy’s high-velocity clouds (HVCs) remains a mystery after many decades of effort. In this paper, we use the TNG50 simulation of the IllustrisTNG project to identify cool, dense clouds that match observations of Galactic H i HVCs. We track these clouds back in time to determine their origin. For a TNG50 Milky Way−like galaxy, we find that only 17% of HVCs can be tracked directly to the disk and 21% to material stripped out of satellites. The majority of HVCs (62%) arise from warm and hot circumgalactic gas that cools through thermal instability. They then obtain their anomalous velocities through interactions with the turbulent circumgalactic medium. At TNG50 resolution, we do not see evidence for HVCs forming out of very low metallicity intergalactic material. Instead, low-metallicity HVCs are most likely associated with satellites. These results suggest that Galactic HVCs are highly heterogeneous in their origin and can provide insight into the physical processes that shape the circumgalactic medium, such as disk outflows, satellite accretion, and thermal instabilities.