This study presents the direct relationships between changes in the annual surface temperature of the North Atlantic (SST) and the number of days per year experiencing low flows in the Warta River catchment (WRC) in Central Europe, Poland, in the multi-annual period of 1951–2020. The number of days experiencing low flows (TLF) was used to describe the conditions of hydrological drought in the WRC. Moderately strong (r~0.5) but statistically highly significant (p < 0.001) relationships were found between TLF and the SST in the subtropical (30–40° N, 60–40° W) and subpolar North Atlantic (70° N, 10° W–10° E). With the increase in the annual SST in these parts of the North Atlantic, the number of days in a year experiencing low flows in the WRC also increased. It was determined that besides synchronous (i.e., in the same year) relationships between TLF and SST, asynchronous relations also occurred: the SST changes were one year ahead of the TLF changes. With the increase in the SST in the subtropical and subpolar North Atlantic, the sunshine duration and air temperature in the WRC increased, while the relative humidity decreased. The relationships between precipitation in the WRC and SST were negative (from −0.04 to −0.14), but statistically insignificant (p > 0.2). This indicates that the impact of SST changes on TLF in the WRC is mainly caused by the shaping of the amount of surface evaporation, which strongly increases in years of high SST, and the climatic water balance becomes negative, resulting in an increase in extremely low flows. The analysis of the causes of these relationships shows that the SST changes in the North Atlantic control, through changes in the height of the geopotential (h500), changes in the atmospheric circulation over Europe. In the periods of SST h500 growth over Central Europe, the atmospheric pressure (SLP) increases. That area is more frequently than average under the influence of the Azores High; this leads to an increase in the frequency of anticyclonic weather. A significant increase in the number of TLFs and prolonged periods of hydrological drought in the WRC after 2000 are associated with a strong increase in the SST in the area of the tropical and subtropical North Atlantic.