Mediterranean water entering the Black Sea through the Bosphorus Strait forms middepth intrusions that contribute to the salt, heat, and volume balances of the sea, ventilate its water column at intermediate depths and restrain the upward flux of hydrogen sulfide from deeper layers. Despite the importance for the Black Sea environment, the circulation of Mediterranean-origin water in the basin is fundamentally underexplored. Here we use hydrographic data collected from ships and Argo profiling floats to identify pathways of the Mediterranean intrusions in the general circulation system of the sea. While earlier the intrusions were observed primarily near the Bosphorus Strait, we present an evidence for their intermittent extensive propagation throughout the basin. We find that the main conduit for the intrusions is the southern limb of the Rim Current that carries the intruded water from the Bosphorus Strait eastward. A part of this eastward flow recirculates cyclonically into the interior of the sea, where traces of the intrusions gradually disappear because of mixing. We put forward the hypothesis that the formation of the most prominent intrusions is associated with strong cyclonic storms over the Bosphorus Strait, which lead to abnormally large influx of Mediterranean water.