Impurity doping of semiconducting nanowires has been predicted to become increasingly inefficient as the wire diameter is reduced, because impurity states get deeper due to quantum and dielectric confinement. We show that efficient n- and p-type doping can be achieved in SiGe core-shell nanowires as thin as 2 nm, taking advantage of the band offset at the Si/Ge interface. A one-dimensional electron (hole) gas is created at the band-edge and the carrier density is uniquely controlled by the impurity concentration with no need of thermal activation. Additionally, SiGe core-shell nanowires provide naturally the separation between the different types of carriers, electron and holes, and are ideally suited for photovoltaic applications.