We studied giant magnetoimpedance (GMI) effect and magnetic properties of FINEMET-type FeCuNbSiB microwires. We observed that the GMI effect and magnetic softness of glass-coated microwires produced by the Taylor–Ulitovski technique can be tailored either controlling magnetoelastic anisotropy of as-prepared FeCuNbSiB microwires or controlling their structure by heat treatment or changing the fabrication conditions. We observed considerable magnetic softening of studied microwires after annealing. This magnetic softening correlates with the devitrification of amorphous samples. Amorphous microwires exhibited low GMI effect (GMI ratio below 5%). Considerable enhancement of the GMI effect (GMI ratio up to 100%) has been observed in heat treated microwires with nanocrystalline structure. Some of as-prepared Fe-rich exhibited nanocrystalline structure and the GMI ratio up to 45%.