Processing by Joule-heating the Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 glass-coated microwire allows considerable improvement of magnetic softness and giant magnetoimpedance (GMI) effect. At optimal joule heating conditions we observed GMI ratio up to 650%. Observed magnetic softening and GMI ratio improvement have been discussed considering magnetic anisotropy induced by Oersted magnetic field during current annealing, internal stresses relaxation and radial distribution of magnetic anisotropy. The analysis of the GMI ratio as a function of the frequency (10–1000 MHz) opens new lights to understand the distribution of the magnetic anisotropy inside the glass-coated microwire. Display omitted •Remarkable mprovement of GMI effect in Co -rich microwires current-annealing.•Considerable enhancement of magnetic softness in current-annealed Co-rich microwires.•Interpretation of current annealing effect considering internal stresses relaxation and induced anisotropy.•Evaluation of magnetic field dependence of skin depth in as-prepared and current-annealed microwires.