YES. The fertile soil in the eastern half of the Fertile Crescent came from the Euphrates and Tigris Rivers. However, the fertile soil in the western half of the Fertile Crescent came the Jordan River and the several small streams that coalesce to form it.
Mesopotamia is the area between the Euphrates and the Tigris. It literally means 'between the rivers'. The Fertile Crescent is a crescent-shaped area that stretches from the Mediterranean coast along the Euphrates and the Tigris to the Persian Gulf.