We consider stochastic influence maximization problems arising in social networks. In contrast to existing studies that involve greedy approximation algorithms with a 63% performance guarantee, our work focuses on solving the problem optimally. To this end, we introduce a new class of problems that we refer to as two-stage stochastic submodular optimization models. We propose a delayed constraint generation algorithm to find the optimal solution to this class of problems with a finite number of samples. The influence maximization problems of interest are special cases of this general problem class. We show that the submodularity of the influence function can be exploited to develop strong optimality cuts that are more effective than the standard optimality cuts available in the literature. Finally, we report our computational experiments with large-scale real-world datasets for two fundamental influence maximization problems, independent cascade and linear threshold, and show that our proposed algorithm outperforms the basic greedy algorithm of Kempe et al. (Proceedings of the ninth ACM SIGKDD international conference on knowledge discovery and data mining, KDD’03, New York, NY, USA, ACM, pp 137–146, 2003).