It was previously proved that the Gödel-type metrics with flat three-dimensional background metric solve exactly the field equations of the Einstein-Aether theory in four dimensions. We generalize this result by showing that the stationary Gödel-type metrics with nonflat background in D dimensions solve exactly the field equations of the Einstein-Aether theory. The reduced field equations are the (Formula presented.) -dimensional Euclidean Ricci-flat and the (Formula presented.) -dimensional source-free Maxwell equations, and the parameters of the theory are left free except (Formula presented.). We give a method to produce exact solutions of the Einstein-Aether theory from the Gödel-type metrics in D dimensions. By using this method, we present explicit exact solutions to the theory by considering the particular cases: ((Formula presented.))-dimensional Euclidean flat, conformally flat, and Tangherlini backgrounds. © 2016, Springer Science+Business Media New York.