The magnetic anisotropy of Fe-rich, thin, amorphous wires is tailored by stress annealing (SA). In particular, the effect of conventional annealing (CA) and SA on the magnetic properties of Fe74B13Si11C2 glass-coated microwires is studied. CA treatment does not significantly change the character of the hysteresis loop. Under certain SA conditions (annealing temperature, T-ann > 300 degrees C; applied stress, sigma > 400 MPa), a transverse magnetic anisotropy is induced: a rectangular hysteresis loop transforms into an inclined one at magnetic-anisotropy fields above 1.000 Am-1. Under tensile stress, the rectangular hysteresis loop of microwires annealed using SA is recovered. Samples subjected to SA show noticeable magnetoimpedance and stress-impedance effects, despite their large magnetostriction. The samples obtained exhibit a high stress sensitivity of their giant magnetoimpedance (GMI) effect and hysteretic properties, allowing the use of the obtained samples in magnetoelastic sensors, and for designing stress-sensitive, tunable composite materials. By varying the time and temperature of such SA, we are able to tailor both the magnetic properties and the GMI of Fe-rich rnicrowires.