Let $\mathcal{L}=-\mathrm{\Delta }+V$ be the Schrödinger operators on ${\mathbb{R}}^n$ with nonnegative potential $V$ belonging to the reverse Hölder class $R{H}_q$ for some $q\ge \frac{n}{2}$. We prove the boundedness of fractional integral operator ${\mathcal{I}}_{\alpha }$ related to the Schrödinger operators $\mathcal{L}$ from strong and weak variable exponent Lebesgue spaces into suitable variable exponent Lipschitz type spaces.