We studied the Giant magnetoimpedance (GMI) effect and magnetic properties of amorphous Fe-Co rich magnetic microwires prepared by the Taylor-Ulitovski technique. We observed that these properties can be tailored either controlling magnetoelastic anisotropy of as-prepared Co-rich microwires or controlling their magnetic anisotropy by heat treatment. High GMI effect even at GHz frequencies has been observed in Co-rich microwires.