We demonstrate integrated optomechanical circuits with high mechanical quality factors prepared from nanocrystalline diamond thin films. Using chemomechanical polishing, the RMS surface roughness of as grown polycrystalline diamond films is reduced below 3 nm to allow for the fabrication of high-quality nanophotonic circuits. By integrating free-standing nanomechanical resonators into integrated optical devices, efficient read-out of the thermomechanical motion of diamond resonators is achieved with on-chip Mach-Zehnder interferometers. Mechanical quality factors up to 28,800 are measured for four-fold clamped optomechanical resonators coupled to the evanescent near-field of nanophotonic waveguides. Our platform holds promise for large-scale integration of optomechanical circuits for on-chip metrology and sensing applications.