This paper describes a blind frequency offset estimator (FOE) with wide frequency range for coherent quadrature amplitude modulation (QAM) receivers. The FOE combines a spectrum-based frequency offset estimation algorithm as a coarse estimator with a frequency offset estimation algorithm using the periodogram as a fine estimator. To establish our design methodology, each block of the FOE is rigorously analyzed by using formulas and the minimum fast Fourier transform (FFT) size that generates a frequency spectrum for both the coarse and fine estimators is determined. The coarse estimator's main feature is that all estimation processes are carried out in the frequency domain, which yields convergence more than five times faster than that of conventional estimators. The estimation frequency range of the entire FOE is more than 1.8 times wider than that of conventional FOEs. Experiments on coherent optical 64-ary QAM (64-QAM) reveal that frequency offset estimation can be achieved under a frequency offset value greater than the highest value of the conventional estimation range.