Increased power transfers over a wide geographical area impact the small-signal stability of the power system, defined as the ability to damp oscillations between generators in different geographical areas. Wide-area control architectures have been proposed to control the generators in order to mitigate these oscillations. Ensuring that all unstable oscillating modes are removed depends on selecting a subset of generators to participate in wide-area control, which is inherently a discrete optimization problem that in the current literature does not have any solution algorithms with provable stability guarantees. In this paper, we present MinGen, a submodular optimization framework for generator selection for small-signal stability. We prove that small-signal stability is achieved when the unstable modes are controllable and observable from the set of selected generators, and map these properties to submodular constraints. We develop a computationally efficient and submodular MinGen algorithm with provable optimality bounds for generator selection, which can be generalized to enhance robustness to communication link failures. We evaluate our approach via a numerical study on the IEEE New England test case.