A technique to eliminate the offset drift in the demodulator circuitry of open-loop interferometric fiber optic gyroscopes is presented. This technique employs a demodulation scheme that uses the area of the negative half-cycles of the output signal of a sinusoidally modulated gyroscope to obtain the angular velocity. We propose an electronic circuitry that periodically reverses the demodulator input, allowing for the acquisition of two samples of the gyroscope signal with the same magnitude and opposite polarities. The angular velocity is obtained from the subtraction of these two samples, suppressing the electronic offset. Experiments showed that the proposed method reduces the demodulator offset drift from 4.4 μV/°C to about 14 nV/°C, which is equivalent to a reduction, from 0.2 deg/h/°C to about 0.0006 deg/h/°C in the tested gyroscope. The proposed technique improved the bias stability of the tested gyroscope from 0.0162 to 0.0071 deg/h.