ZrO2 and HfO2 powder samples were prepared by using the chemical precipitation method and subsequent annealing. Crystal structure, local electronic structure and dielectric constant of amorphous and crystalline powders of ZrO2 and HfO2 have been examined using the synchrotron X-ray diffraction, O K-edge X-ray absorption spectroscopy, Zr 3d and Hf 4f core-level X-ray photoelectron spectroscopy and temperature dependent dielectric measurements, respectively. Amorphous ZrO2 and HfO2 powders exhibit a local tetragonal structure, with mixed +3 and +4 valence states of Zr and Hf ions, and demonstrated the high dielectric performance. After the heat treatment, the tetragonal phase transforms into the monoclinic phase with dominant +4 valence state of Zr and Hf ions and the larger sized ZrO2 and HfO2 nanoparticles exhibited low dielectric constant. The manifestation of high dielectric constants in the amorphous ZrO2 and HfO2 samples is because of the hopping of electrons between the Zr +3 -Zr +4 and Hf +3 -Hf +4 networks.