We present a novel statistical moments-based method for optical signal-to-noise ratio (OSNR) monitoring in polarization-multiplexed (pol-mux) coherent optical systems. This technique only requires the knowledge of the envelope of the equalized signal before phase correction, which can be achieved by using any two arbitrary statistical moments, and it is suitable for both constant and non-constant modulus modulation formats. The proposed estimation method is experimentally demonstrated for 10-Gbaud pol-mux coherent systems using QPSK and 16-QAM. Additionally, numerical simulations are carried out to demonstrate 20-Gbaud systems using 16-QAM and 64-QAM. The results show that the OSNR can be estimated accurately over a wide range of values for QPSK, 16-QAM or 64-QAM systems up to 1920-km long and with up to 50-ps all-order polarization mode dispersion. By setting a proper reference value for calibration, the proposed algorithm also shows good tolerance when the received signal is not well compensated.