In this study, a simple, inexpensive, scalable solution combustion process devoid of toxic chemicals is suggested for the synthesis of ZnO and CeO2 nanostructures. Different techniques were used to characterize the morphologies, crystal phases, purity and composition of as-synthesized nanostructures. For ZnO nanoparticles, field emission scanning electron microscopy examination revealed spheroidal, elongated hexagonal rods, triangular and pentagonal morphologies, whereas for CeO2, sheet-like morphologies with various thicknesses were observed. X-ray diffraction investigation indicated wurtzite hexagonal and cubic fluorite phases for ZnO nanoparticles and CeO2 nanosheets with crystallite sizes of 49.50 and 11.04 nm, respectively. Energy dispersive X-ray spectrometry, electron mapping and elemental distribution images confirmed the purity of the synthesized nanostructures. The optical bandgap of ZnO nanoparticles and CeO2 nanosheets were found to be 3.28 and 3.55 eV, respectively. ZnO nanoparticles and CeO2 nanosheets demonstrated outstanding photocatalytic efficiencies for the degradation of model dyes like Congo red (CR), rhodamine (RhB) and methylene blue (MB). However, ZnO nanoparticles outperformed CeO2 nanosheets in photodegradation. Under UV-light irradiation, the degradation rate of the dyes was reduced in the following sequence for both photocatalysts: CR > MB > RhB. The low degradation efficiency of CeO2 nanosheets can be attributed to their higher bandgap energy as compared to ZnO nanoparticles. Further, photocatalytic degradation of different dyes followed Langmuir-Hinshelwood pseudo-first-order kinetic model. The exceptional dye-degrading abilities of the as-synthesized nanostructures, synthesized using the combustion process, show that they are suited for photocatalysis applications.