This paper presents the design and implementation of a high sensitivity giant magnetoresistance (GMR) based current sensor with a broad range of applications. The novelty of our approach consists in using a double differential measurement system, based on commercial GMR sensors, with an adjustable biasing system used to linearize the field response of the system. The work aims to act as a fully-operational proof of concept application, with an emphasis on the mode of operation and methods to improve the sensitivity and linearity of the measurement system. The implemented system has a broad current measurement range from as low as 75 mA in DC and 150 mA in AC up to 4 A by using a single setup. The sensor system is also very low power, consuming only 6.4 mW. Due to the way the sensors are polarized and positioned above the U-shaped conductive band through which the current to be measured is flowing, the differential setup offers a sensitivity of about between 0.0272 to 0.0307 V/A (signal from sensors with no amplifications), a high immunity to external magnetic fields, low hysteresis effects of 40 mA, and a temperature drift of the offset of about −2.59×10−4 A/°C. The system provides a high flexibility in designing applications where local fields with very low amplitudes must be detected. This setup can be redesigned for a wide range of applications, thus allowing further specific optimizations, which would provide an even greater accuracy and a significantly extended operation range.