In this paper, we study the optimal location planning of renewable distributed generation (RDG) units by taking into account the random uncertainties of renewable generation and load demand. In presence of the random uncertainties, location planning problem is naturally a two-stage stochastic mixed integer nonlinear programming problem, which is hard to solve efficiently. Instead of using traditional sampling methods or robust optimization methods, we propose a novel analytical approach in this paper to solve the problem efficiently and optimally. In particular, analytical expressions are derived for efficiently evaluating the performance of a candidate RDG placement decision. In this way, the stochastic mixed integer nonlinear programming problem is equivalently transformed into a deterministic integer problem, which can be solved efficiently using off-the-shelf tools. Numerical results show that the optimal RDG placement can save up to $4.2\%$ of the long-term average cost and $80.59\%$ of the line losses on the IEEE 13-bus test feeder. In addition, our proposed approach effectively reduces the computational time by $99.51\%$ on the IEEE 123 node test feeder compared with other traditional sampling-based metaheuristic approaches.