  It was previously proved that the G\"{o}del-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 G\"{o}del-type metrics with nonflat background in $D$
dimensions solve exactly the field equations of the Einstein-Aether theory. The
reduced field equations are the $(D-1)$-dimensional Euclidean Ricci-flat and
the $(D-1)$-dimensional source-free Maxwell equations, and the parameters of
the theory are left free except $c_{1}-c_{3}=1$. We give a method to produce
exact solutions of the Einstein-Aether theory from the G\"{o}del-type metrics
in $D$ dimensions. By using this method, we present explicit exact solutions to
the theory by considering the particular cases: ($D-1$)-dimensional Euclidean
flat, conformally flat, and Tangherlini backgrounds.
