Alloy composition (Co94Fe6)72.75Si12.25B13.25Cr1.75 was designed to develop nearly zero-magnetostrictive materials in the form of ribbons and wires to obtain suitable magnetic properties for use as giant magnetoimpedance (GMI) and low-noise fluxgate sensor cores. During the development of magnetic sensing core using amorphous wires of diameter 80 $\mu \text{m}$ for GMI sensing, we observed a maximum impedance change (GMI ratio) of 430% with as-cast wires, which further enhanced to 650% when annealed at 300 °C for 5 min. The effect of annealing temperature and stress on the magnetic properties of fluxgate sensing core materials has been studied. Magnetic hysteresis loops were measured with 3-mm-wide and 45- $\mu \text{m}$ -thick amorphous ribbons on a toroidal ring of 50 mm diameter for fluxgate sensor core. A coercivity of 10.57 A/m and saturation field of $\sim$ 150 A/m were observed with as-quenched ribbon, which improved to a coercivity of 2.16 A/m and saturation field $\sim$ 100 A/m when annealed without stress just above its Curie temperature. An induced anisotropy transverse to excitation direction was achieved by applying temperature with stress and time (300 °C/ 100 MPa/ 20 min) to use it for fluxgate sensor core.