Identification of prominent sea areas for the efficient exploitation of offshore wind energy potential requires primarily the assessment and modeling of several aspects of the long-term wind climate. In this work, the offshore wind speed and wind direction climate of the Mediterranean Sea is analytically described, the corresponding offshore wind energy potential is estimated on an annual and seasonal basis, and candidate areas for potential offshore wind farm development are identified. The analysis is based on ocean surface wind fields obtained from the Blended Sea Winds product, provided by the U.S. National Oceanic and Atmospheric Administration (NOAA), from 1995 to 2014. The satellite data are evaluated with reference to buoy wind measurements in the Spanish and Greek Seas. Wind data analysis reveals areas in the western and eastern Mediterranean Sea with high mean annual wind speed combined with rather low temporal variability. The obtained results suggest that offshore wind power potential in the Mediterranean Sea is fairly exploitable at specific suitable locations, such as the Gulf of Lions (with mean annual wind power density up to $\sim $ 1600 W/m ${}^{2}$ ) and the Aegean Sea (with mean annual wind power density up to $\sim $ 1150 W/m ${}^{2}$ ), that are certainly worth further in-depth assessment for exploiting offshore wind energy. Finally, based on the available offshore wind resource potential and the water depth suitability, three specific sites (in the Gulf of Valencia and the Adriatic and Ionian Seas) are selected and the average wind power output for a specific wind turbine type is estimated.