Let $X$ be a compact connected Kähler manifold of complex dimension $n$, let $\omega$ be a Kähler form on $X$, and let $\rho$ be a smooth closed real $(1,1)$-form whose de Rham cohomology class is $2\pi c_1(X)$. Then there exists a unique Kähler form $\omega'$ on $X$ such that $\omega'$ lies in the Kähler class $[\omega]$ and $\operatorname{Ric}(\omega')=\rho$.