High-statistics differential cross sections for the reactions gamma p -> p eta and gamma p -> p eta' have been measured using the CEBAF large acceptance spectrometer (CLAS) at Jefferson Lab for center-of-mass energies from near threshold up to 2.84 GeV. The eta' results are the most precise to date and provide the largest energy and angular coverage. The. measurements extend the energy range of the world's large-angle results by approximately 300 MeV. These new data, in particular the eta' measurements, are likely to help constrain the analyses being performed to search for new baryon resonance states.