OSNR monitoring is indispensable for coherent systems to ensure robust, reliable network operation and potentially enable impairment-aware routing for future dynamic optical networks. In a long-haul transmission link with chromatic dispersion (CD) and fiber nonlinearity, it is difficult to distinguish between amplifier noise and fiber nonlinearity induced distortions from received signal distributions even after various transmission impairment compensation techniques, thus resulting in grossly inaccurate OSNR estimates. Based on the received signal distributions after carrier phase estimation (CPE), we propose to characterize the nonlinearity-induced amplitude noise correlation across neighboring symbols and incorporate such information into error vector magnitude (EVM) calculation to realize fiber nonlinearity-insensitive OSNR monitoring. For a transmission link up to 1600 km and signal launched power up to 2 dBm, experimental results for 112 Gb/s polarization-multiplexed quadrature phase-shift keying (PM-QPSK) demonstrate an OSNR monitoring range of 10-24 dB with a maximum estimation error below 1 dB. For 224 Gb/s PM-16-quadrature amplitude modulation (PM-16-QAM) systems, simulation results demonstrate an OSNR monitoring range of 18-28 dB with a maximum estimation error below 1 dB. Tolerance of the proposed OSNR monitoring technique to different pulse shapes, timing phase offsets, polarization dependent loss (PDL), polarization-mode dispersion (PMD) and WDM effects are also investigated through simulations.