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The linkage between atmospheric blocking (blocking frequency, BF) and total monthly July precipitation in the Selenga River Basin, the main tributary of Lake Baikal, for the period 1979–2016 was investigated. Based on empirical orthogonal functions (EOF) analysis, two dominant modes of precipitation over the Selenga River Basin were extracted. The first EOF mode (EOF 1) is related to precipitation fluctuations mainly in the Mongolian part of Selenga; the second EOF mode (EOF 2)—in the Russian part of Selenga. Based on two different modes obtained, the total amount of precipitation individually for the Russian and Mongolian part of Selenga was calculated. Correlation analysis has demonstrated that precipitation over the Mongolian part of the Selenga Basin is positively correlated to blocking over Eastern Siberia/Mongolia (80–120° E, ESM-BF). Precipitation over the Russian part of the Selenga Basin is positively correlated to blocking over the Urals-Western Siberia (50–80° E, UWS-BF) and European blocking (0–50° E, E-BF). However, the linkage is not stable, and after the mid-1990s, the obtained positive correlation became insignificant. The analysis has shown that the dominance of E or ESM-blocking in July was the primary driver of the existence of two precipitation modes over the Selenga River Basin. During 1996–2016, the negative trend of time coefficients of EOF 1 and 2 for precipitation in Selenga had been observed, which was characterized by displacement of positive precipitation anomalies outside the basin. At the same time, there was a weakening of the linkage between precipitation in the Selenga Basin and blocking frequency. We have revealed two wave-like modes over Northern Eurasia and the subtropical part of Eurasia corresponding to E, ESM-blocks in 1979–1995 and 1996–2016. The change of the Northern and subtropical wave modes is one of the causes for the weakening of the linkage between atmospheric blocking and precipitation in the Selenga Basin and as a consequence decreased precipitation in the Russian and Mongolian part of Selenga during 1979–2016. [ABSTRACT FROM AUTHOR]