This Thesis aimed at developing a high sensitivity magnetometer, based on the phase characteristics of the Giant Magnetoimpedance effect (GMI), for measuring ultra-weak magnetic fields. GMI sensor elements have great potential to implement magnetometers that combine high sensitivity and high spatial resolution with low cost. The optimization of the magnetic transducer sensitivity is directly affected by the sensitivity of its GMI sensor elements, whose maximization is inherently multivariate. Consequently, the first step of the experimental methodology employed was to develop an automatic system for the characterization of GMI samples, so as to ensure the agility of the characterization process, allowing the gathering of a significant amount of experimental data. A thorough analysis of the experimental data led to the definition of the optimal operation point of the analyzed GMI samples. The hysteresis curves of the GMI samples were obtained and evaluated, in all of the performed experimental measurements. Based on the characterization studies results, electronic circuits were designed for conditioning the GMI samples and reading their impedance phase characteristics, highlighting the new electronic configuration developed for enhancing the phase sensitivity. National and international patents were filed, related to the proposed method, for sensitivity enhancement, and to the new GMI magnetometer (PI 0902770-0; PI 1004686-0; WO/2010/094096 e WO/2012/048395). The performed experimental characterizations and assays indicated the effectiveness of the proposed approach, showing the great potential of the developed GMI magnetometer, which presents a high sensitivity of 5 mV/nT. The magnetometer resolution was limited by the environmental magnetic noise, pointing out their capability in measuring fields below the environmental noise level, which can be clearly evidenced only when evaluated in a magnetically shielded room. The theoretical and experimental studies carried out indicate the potential of the developed GMI magnetic transducer, characterized by its low cost and high sensitivity, for applications involving the measurement of ultra-weak magnetic fields.