Semiconductor nanowires are potential candidates for applications in quantum information processing(1,2), Josephson junctions(3,4) and field-effect transistors(5-8) and provide a unique test bed for low-dimensional physical phenomena(9). The ability to fabricate nanowire heterostructures with atomically flat, defect-free interfaces enables energy band engineering in both axial(10-12) and radial(13-16) directions. The design of radial, or core-shell, nanowire heterostructures relies on energy band offsets that confine charge carriers into the core region, potentially reducing scattering from charged impurities on the nanowire surface(13-16). Key to the design of such nanoscale heterostructures is a fundamental understanding of the heterointerface properties, particularly energy band offsets and strain. The charge-transfer and confinement mechanism can be used to achieve modulation doping(17-19) in core-shell structures(20,21). By selectively doping the shell, which has a larger bandgap, charge carriers are donated and confined in the core, generating a quasi-one-dimensional electron system with higher mobility. Here, we demonstrate radial modulation doping in coherently strained Ge-SixGe1-x core-shell nanowires and a technique to directly measure their valence band offset. Radial modulation doping is achieved by incorporating a B-doped layer during epitaxial shell growth. In contrast to previous work showing site-selective doping in Ge-Si core-shell nanowires(13,22), we find both an enhancement in peak hole mobility compared with undoped nanowires and observe a decoupling of electron transport in the core and shell regions. This decoupling stems from the higher carrier mobility in the core than in the shell and allows a direct measurement of the valence band offset for nanowires of various shell compositions.