In this Letter, we introduce a graded-index (GRIN)-lens combination named GRIN-axicon, which is a versatile component capable of generating high-quality scalable Bessel-Gauss beams. To the best of our knowledge, the GRIN-axicon is the only optical component that can be introduced in both larger-scale laboratory setups and miniaturized all-fiber optical setups, while having an easy control of the dimensioning of the generated focal line. We show that a GRIN lens with a hyperbolic secant refractive index profile with a sharp central dip and no ripples generates a Bessel-Gauss beam with a high-intensity central lobe when coupled to a simple lens. Such fabrication characteristics are very suitable for the modified chemical vapor deposition (MCVD) process and enable easy manufacturing of an adaptable component that can fit in any optical setup.