Power gating is a very effective method in reducing the leakage energy during the standby mode in VLSI circuits at the cost of increased circuit delay. This method has been well studied and widely used for circuits fabricated by using traditional CMOS technology nodes operating at super-threshold supply voltage regime. However, for advanced technology nodes with small feature sizes and low supply voltages, the propagation delay becomes very sensitive to the high process-induced variations. Therefore, this paper first analyzes how the circuit delay depends on the size of the sleep transistor under the process-induced variation for the 7nm gate length FinFET technology. Then a joint optimization problem is formulated to minimize the total energy consumption, while both supply voltage and sleep transistor size are considered as optimization variables. A near-optimal heuristic is presented to solve the optimization problem and determine the energy-optimal supply voltage and sleep transistor size. Experimental results based on HSPICE simulations show that more than 98% energy reduction for applications with relaxed deadline constraints after applying the joint optimization technique, compared to FinFET circuits without using the power gating method.