Bessel-Gauss beams have mainly been proposed in optics as a solution for reducing the on-axis intensity oscillations typical of Bessel beams. Previous investigations on Bessel-Gauss beams are based on a scalar theory in the paraxial approximation, and thus cannot be extended to the microwave range where a fully vectorial approach is needed. Here, the generation of Bessel-Gauss beams through leaky waves is investigated. First, the nondiffractive and focusing properties of Bessel-Gauss beams generated through leaky waves are extensively examined in the frame of a vectorial approach. Useful design criteria are derived to optimize both the radiation and the focusing efficiency of such beams. On this basis, leaky-wave radiators synthesized to support the generation of a Bessel-Gauss beam over a given frequency band in the microwave range are presented. Full-wave results corroborate the concept.