In the present work, we report the synthesis of high quality ZnO nanocrystals with sharp absorption edges in four different sizes, namely 3.0, 3.5, 4.7 and 5.4 nm, characterized by X-ray and electron diffraction, as well as transmission electron microscopy. The bandgaps of these samples, in conjunction with further data from the published literature, exhibit a systematic dependence on the nanocrystal size. In absence of any prior reliable theoretical results in the literature to understand this dependence quantitatively, we have analyzed for the first time, the electronic structure of bulk ZnO obtained from the full potential linearized augmented plane wave method using fatbands, density of states and partial density of states. The crystal orbital Hamiltonian population is obtained from linearized Muffin-Tin orbital band structure calculations to understand the range of hopping interactions relevant for an accurate description of the electronic structure. Using these analyses, a realistic tight binding model is proposed. Based on this model, we calculate the variation of the bandgap with the size of ZnO nanocrystals. These theoretical results agree well with all available data over the entire range of sizes, establishing the effectiveness of this approach.