Linear Temporal Logic (LTL) synthesis can be understood as the problem of building a controller that defines a winning strategy, for a two-player game against the environment, where the objective is to satisfy a given LTL formula. It is an important problem with applications in software synthesis, including controller synthesis. In this paper we establish the correspondence between LTL synthesis and fully observable non-deterministic (FOND) planning. We study LTL interpreted over both finite and infinite traces. We also provide the first explicit compilation that translates an LTL synthesis problem to a FOND problem. Experiments with state-of-the-art LTL FOND and synthesis solvers show automated planning to be a viable and effective tool for highly structured LTL synthesis problems.