  In this paper we give a complete characterization of Morita equivalent star
products on symplectic manifolds in terms of their characteristic classes: two
star products $\star$ and $\star'$ on $(M,\omega)$ are Morita equivalent if and
only if there exists a symplectomorphism $\psi:M\longrightarrow M$ such that
the relative class $t(\star,\psi^*(\star'))$ is $2 \pi \im$-integral. For star
products on cotangent bundles, we show that this integrality condition is
related to Dirac's quantization condition for magnetic charges.
