To study the nature of climate change in the hydrometeorological parameters of the Black and Azov Seas—surface air temperature (SAT), sea surface temperature (SST), ice cover, and sea level—under conditions of ongoing global warming, we used reanalyses and remote sensing data, as well as information from known publications of recent years. It was found that against an increase in SAT over the Black–Azov Sea region (+0.053°C/year in 1980–2020) and SST of the Black Sea (+0.052°C/year in 1982–2020), the values of these parameters in the 2000s differ significantly from those in the 1980s–1990s: the maximum average monthly summer and minimum average monthly winter temperatures have increased, as well as the number of mild winters. The average annual SST of the Black Sea, which practically did not exceed 15°C in the 1980s–early 1990s, has exceeded 16°C in most cases since 2010 (maximum 16.71°C in 2018). In the 2010s, the average monthly winter minima, with the exception of the winters of 2011/2012 and 2016/2017, did not fall below 8°С. A consequence of the increase in winter temperatures was a decrease in the ice concentration in the Sea of Azov (the trend of the mean monthly concentration is –1.2%/10 years). From about 2004–2010 in the Black Sea and since 2004 in the Sea of Azov, the tendency towards increase in their levels (on average) has been replaced by a slight decrease, so that the average positive trends for the period 1993–2020 (+0.32 ± 0.16 cm/year in the Black Sea and +0.21 ± 0.05 cm/year in the Sea of Azov) were approximately 2.5 times less than in 1993–2012. The reason for this decrease in levels (on average) in the last 10–15 years was apparently a decrease in the incoming part of the freshwater balance of both seas, which is indirectly confirmed by the observed increase in salinity of their waters.