Synchronization underlies phenomena including memory and perception in the brain, coordinated motion of animal flocks, and stability of the power grid. These synchronization phenomena are often modeled through networks of phase-coupled oscillating nodes. Heterogeneity in the node dynamics, however, may prevent such networks from achieving the required level of synchronization. In order to guarantee synchronization, external inputs can be used to pin a subset of nodes to a reference frequency, while the remaining nodes are steered toward synchronization via local coupling. In this paper, we present a submodular optimization framework for selecting a set of nodes to act as external inputs in order to achieve synchronization from a desired set of initial states. We derive threshold-based sufficient conditions for synchronization, and then prove that these conditions are equivalent to constraints on monotone submodular functions over partition matroids. Based on this connection, we map the sufficient conditions for synchronization to constraints on submodular functions, leading to efficient algorithms with provable optimality bounds for selecting input nodes. We illustrate our approach via numerical studies of synchronization in power systems.