The problem of mercury input and its further distribution in the Arctic environment is actively debated, especially in recent times, due to the observed processes of permafrost thawing causing the enhanced release of mercury into the Arctic atmosphere and further distribution in the terrestrial and aquatic ecosystem. The atmospheric mercury deposition occurs via dry deposition and wet scavenging by precipitation events. Here we present a study of Hg in wet precipitation on the remote territory of the Russian Arctic; the data were obtained at the monitoring stations Nadym and Salekhard in 2016–2018. Mercury pollution of the Salekhard atmosphere in cold time is mainly determined by regional and local sources, while in Nadym, long-range transport of mercury and local fuel combustion are the main sources of pollutants in the cold season, while internal regional sources have a greater impact on the warm season. Total mercury concentrations in wet precipitation in Nadym varied from <0.5 to 63.3 ng/L. The highest Hg concentrations in the springtime were most likely attributed to atmospheric mercury depletion events (AMDE). The contributions of wet atmospheric precipitation during the AMDE period to the annual Hg deposition were 16.7% and 9.8% in 2016/2017 and 2017/2018, respectively. The average annual volume-weighted Hg concentration (VWC) in the atmospheric precipitation in Nadym is notably higher than the values reported for the remote regions in the Arctic and comparable with the values obtained for the other urbanized regions of the world. Annual Hg fluxes in Nadym are nevertheless close to the average annual fluxes for remote territories of the Arctic zone and significantly lower than the annual fluxes reported for unpolluted sites of continental-scale monitoring networks of the different parts of the world (USA, Europe, and China). The increase of Hg deposition flux with wet precipitation in Nadym in 2018 might be caused by regional emissions of gas and oil combustion, wildfires, and Hg re-emission from soils due to the rising air temperature. The 37 cm increase of the seasonally thawed layer (STL) in 2018 compared to the 10-year average reflects that the climatic changes in the Nadym region might increase Hg(0) evasion, considering a great pool of Hg is contained in permafrost.