Focused electron beam induced deposition (FEBID) is considered the ultimate direct-write lithography technique for three-dimensional (3D) structures.However, it has not been possible yet to obtain 3D deposits by FEBID with the same purity and crystallinity of the corresponding bulk materials. In the present work, purified and crystalline 3D cobalt nanowires of diameter below 90 nm have been fabricated by ex-situ high-vacuum annealing at 600 ºC after FEBID growth. While increasing the metallic content of the nanowires up to 95% at., the thermal annealing process induces the recrystallization of the pseudo-amorphous as-grown structure into bulk-like, hcp and fcc crystallites with lateral sizes comparable to the nanowire's width. The net magnetization increases 80% with respect to as-grown values, up to 1.61 0.06 T, near bulk cobalt. This achievement opens new pathways for applications of this synthetic method in the fabrication of either individual or arrays of 3D high-purity and crystalline cobalt nanowires for high-density memory and logic devices, nanosensors and actuators, and could be a viable method to obtain other pure and crystalline 3D materials by FEBID.