We introduce a new method for adaptive one-bit quantization of linear measurements and propose an algorithm for the recovery of signals based on generalized approximate message passing (GAMP). Our method exploits the prior statistical information on the signal for estimating the minimum-mean-squared error solution from one-bit measurements. Our approach allows the one-bit quantizer to use thresholds on the real line. Given the previous measurements, each new threshold is selected so as to partition the consistent region along its centroid computed by GAMP. We demonstrate that the proposed adaptive-quantization scheme with GAMP reconstruction greatly improves the performance of signal and image recovery from one-bit measurements.