We report on ab-initio DFT/FP-LAPW/TB-mBJ/GGA and LDA investigation of structural and electronic properties of MgxZn1−xO alloys in Würtzite (WZ), Rocksalt (RS) and Zinc-Blende (ZB) phases. TB-mBJ corrections of electronic exchange and correlation interactions make it possible to improve considerably the computational results which we have found very close to the experimental data. As expected, our results show that at 0.375 < x < 0.5, MgxZn1−xO undergoes a phase transition from the tetrahedrally coordinated non-centrosymmetric covalent WZ phase to the octahedrally coordinated ionic RS phase, and the ZB phase remains metastable in the whole 0 ≤ x≤1 range. Our structural properties results show that the lattice parameters vary nonlinearly with x in all three phases. In ZB phase, aZB increases with x very slightly (ΔaZB/aZB≤+0.6%) while in RS phase, aRS decreases with x more strongly (ΔaRS/aRS ≈ −1.7%). The strongest lattice parameters variations with x are found in WZ phase where increasing x results in increasing aWZ (ΔaWZ/aWZ≈+1.4%), decreasing cWZ (ΔcWZ/cWZ ≈ −2.9%), decreasing cWZ/aWZ ratio (Δ(cWZ/aWZ)/(cWZ/aWZ)≈-3.31%), and increasing u internal parameter (Δu/u≈+2.8%). Our electronic properties results show that the fundamental energy bandgap EG is Γ-direct in WZ and ZB MgxZn1−xO in the whole 0 ≤ x≤1 range. In RS MgxZn1−xO, EG is indirect throughout 0 ≤ x < 1 range including RS ZnO and excluding RS MgO where EG is Γ-direct. In all three phases, EG increases with x first linearly in the low x range (x < 0.5), then nonlinearly at higher x (x≥0.5). At x < 0.5, EGZB(x) = 2.609 + 2.861×x eV, EGWZ(x) = 2.863 + 1.990x eV, and EGRS(x) = 3.190 + 1.508x eV. At x≥0.5, nonlinear EG(x) variations show strong bowing parameters depending on the crystal phase: bZB = 2.709eV, bWZ = 4.079eV, and bRS = 16.83eV. These strong EG(x) variations which are confined to a narrow high x range, are tightly correlated with the addition of Zn to MgO and are the strongest in RS MgxZn1−xO. Densities of states and energy band structure data analysis show dominant influence of strong exchange and correlation interactions between hybridized O:2p-Zn:3d orbitals which take place as soon as Zn is introduced into MgO. Our results confirm early findings that O:2p-Zn:3d interactions do play a leading role in overall MgxZn1−xO physical properties whatever the phase, with strongest effects in RS phase, especially in huge EG bowings and in RS-WZ phase transition.