We present an ab initio formalism for the calculation of transport properties in compositionally disordered systems within the framework of the Korringa-Kohn-Rostoker nonlocal coherent potential approximation. Our formalism is based on the single-particle Kubo-Greenwood linear response and provides a natural means of incorporating the effects of short-range order upon the transport properties. We demonstrate the efficacy of the formalism by examining the effects of short-range order and clustering upon the transport properties of disordered AgPd and CuZn alloys.