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The Arctic rivers contribute more than one‐third of the total freshwater streamflow into the Arctic Ocean and play an essential role in the heat and mass circulation of the Arctic atmosphere/ocean system. As the Arctic is warming faster than the global average, the streamflow from Arctic basins increases. This study analyzed the streamflow of the three largest Siberian rivers: the Lena, Yenisei, and Ob', at multiple temporal scales. Results show that the annual streamflow of each river basin exhibits statistically significant increasing trends, while the seasonal streamflow of sub‐basins generally decreases in the summer but increases in the winter. Both autocorrelation and long‐term persistency are often found in the streamflow time series, which indicates significant changes in the large‐scale climatological environment. Therefore, wavelet coherence between the streamflow and large‐scale climate patterns, including the El Niño–Southern Oscillation (ENSO), North Pacific pattern (NP), Arctic Oscillation (AO), and the Pacific/North America Pattern (PNA), have been conducted. NP and ENSO are found to have positive relationships with the precipitation and the ratio of potential evapotranspiration over the precipitation. AO and the PNA are found to have positive relationships with the streamflow of the Ob' and Yenisei rivers at decadal and multidecadal scales. This study demonstrates that the existence of nonstationarities within the Siberian streamflow as the combined impact of climate change alters the hydroclimatological and terrestrial environment of Siberia. These findings provide new insights into the mechanisms underlying the hydrologic changes to warming trends and oscillations of climate patterns, which contribute to our understanding and the prediction of streamflow of these northern rivers. [ABSTRACT FROM AUTHOR]