Analyticity up to the boundary for the divergence equation

We address analytic regularity for the divergence equation $\text{div}\, u = f$ in $\Omega$, with $u=0$ on $\partial\Omega$, where $\Omega$ is an arbitrary bounded analytic domain and $\int_{\Omega} f\,dx=0$. If $f$ is analytic on the closure of $\Omega$, then we prove that there exists a solution that is analytic on the closure of $\Omega$.