The major sources of atmospheric moisture over the Red Sea are analyzed using ERA-Interim for the 1979-2013 period. The vertical structure of moisture transports across the coastlines has been computed separately for the western and eastern coasts of the Red Sea. The vertical structure of the moisture transport from the Red Sea to the continents is dominated by a breeze-like circulation in the near-surface layer and the Arabian high above 850 hPa. The lower-layer, breeze-like circulation is acting to export the moisture to the northwest of Africa and to the Arabian Peninsula and contributes about 80% of the moisture exports from the Red Sea, dominating over the transport in the upper layer, where the moisture is advected to the Arabian Peninsula in the northern part of the sea and to the African continent in the southern part. Integrated moisture divergence over the Red Sea decreased from the early 1980s to 1997 and then increased until the 2010s. Associated changes in the moisture export were provided primarily by the increasing intensity of the breeze-associated transports. The transports above the boundary layer, while being strong across the western and the eastern coasts, have a smaller effect on the net moisture export. The interannual variability of the moisture export in the near-surface layer was found to be closely correlated with the variability in sea surface temperature, especially in summer. Implications of the observed changes in the moisture advection for the hydrological cycle of the Middle East are discussed.