We present the development of the achromatic nanostructured micro-optical component and numerical analyses of its performance for generating optical vortex beams with a single topological charge. The proposed structure was developed using two desired thermally matched glasses suitable for realization using the cost-effective modified stack-and-draw method. As a proof of concept, we conducted numerical studies for a selected free-space achromatic vortex phase structure with a thickness of about 60 µm. The simulation results verified the generation of vortex beams with a single topological charge at the mode-conversion efficiency of 100% at two typical laser wavelengths, 633 and 1000 nm. Moreover, the proposed element also allows correction of the chromatic aberration with a high mode-conversion efficiency of more than 90% over 605–1165 nm.