No. The Tigris and Euphrates rivers originate in Turkey, flow through Syria and Iraq, and converge to form the Shatt al-Arab, which empties into the Persian Gulf—not the Mediterranean Sea.
This river system defines Mesopotamia ("land between the rivers"), the cradle of ancient Sumerian, Babylonian, and Assyrian civilizations. Their delta in southern Iraq creates vast wetlands critical for biodiversity and human history alike.