This paper proposes a double-time-scale coordinated voltage control scheme for distribution networks with distributed generators (DGs) based on model predictive control (MPC) to regulate the voltage profile across a network. The slow-time-scale control scheme is designed to correct long-term voltage deviations while reducing the number of actions of the on-load tap changer, step voltage regulators, and capacitor banks. The MPC problem is formulated as a mixed-integer quadratic programming (MIQP). A tailored exaction solution method based on the branch-and-bound algorithm embedded with an alternating direction method of multiplier-based QP solver is developed to efficiently solve the MIQP problem. In the fast-time-scale control, the active and reactive power outputs of DGs are optimally coordinated to handle the fast voltage fluctuations as well as capture more renewable energy. An efficient analytical sensitivity calculation method is used to update the voltage sensitivities online. The effectiveness of the proposed control scheme along with the exact solution method is verified on a modified real 20 kV distribution system.