Intrinsically disordered proteins (IDPs) are involved in a wide variety of physiological and pathological processes and are best described by ensembles of rapidly interconverting conformers. Using fast field cycling relaxation measurements we here show that the IDP alpha-synuclein as well as a variety of other IDPs undergoes slow reorientations at time scales comparable to folded proteins. The slow motions are not perturbed by mutations in alpha-synuclein, which are related to genetic forms of Parkinson's disease, and do not depend on secondary and tertiary structural propensities. Ensemble-based hydrodynamic calculations suggest that the time scale of the underlying correlated motion is largely determined by hydrodynamic coupling between locally rigid segments. Our study indicates that long-range correlated dynamics are an intrinsic property of IDPs and offers a general physical mechanism of correlated motions in highly flexible biomolecular systems.