We consider discretizations of the singularly perturbed Oseen equations on properly layer-adapted meshes. Using a suitable solution decomposition, we are able to prove optimal convergence orders in the associated energy norm for grad-div stabilized finite element methods in a general setting. Two families of pairs of discrete function spaces, namely Q_k × Q_k−₁ and Q_k × P_k^disc₋1, k ≥ 2, are investigated in detail. The usage of a standard nonstabilized Galerkin method reduces the order by 1 while stabilization outside the layers is enough to regain the full optimal order.