The Cornell Electron-positron Storage Ring (CESR) has been converted from a High Energy Physics electron-positron collider to operate as a dedicated synchrotron light source for the Cornell High Energy Synchrotron Source (CHESS) and to conduct accelerator physics research as a test accelerator, capable of studying topics relevant to future damping rings, colliders and light sources. Some of the specific topics that were targeted for the initial phase of operation of the storage ring in this mode, labeled CesrTA (CESR as a Test Accelerator), included 1) tuning techniques to produce low emittance beams, 2) the study of electron cloud development in a storage ring and 3) intra-beam scattering effects. The complete conversion of CESR to CesrTA occurred over a several year period, described elsewhere. As a part of this conversion the CESR beam position monitoring (CBPM) system was completely upgraded to provide the needed instrumental capabilities for these studies. This paper describes the new CBPM system hardware, its function and representative measurements performed by the upgraded system.