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Silicon germanium (SiGe) semiconductors are driving our modern society based on electronic processing devices. However, the inherent indirect bandgap alignment of SiGe prohibits efficient light emission. Crystal phase engineering of SiGe semiconductors allows for direct bandgap hexagonal 2H, 4H, and 6H polytypes. Here, we report the growth of 4H-Ge and 4H-SiGe nanowires with high crystal phase purity. We exploit crystal structure transfer by epitaxial growth of 4H-SiGe nanowires on a 4H-ZnS substrate. Although theory predicts that 4H-Ge exhibits a parity-forbidden fundamental transition, we report direct bandgap light emission from both 4H-Ge and 4H-SiGe nanowires, as well as tunability of the emission wavelength with composition. We find effective recombination lifetimes of 55 and 400 μs for 4H-Ge and 4H-Si0.2Ge0.8, respectively. We finally observe excellent agreement between ab initio density functional theory and experiment on the bandgap and the radiative lifetimes of the 4H-SiGe alloys.