Electrodynamic responses from three-dimensional (3D) topological insulators (TIs) are characterized by the universal magnetoelectric $E\cdot B$ term constituent of the Lagrangian formalism. The quantized magnetoelectric coupling, which is generally referred to as topological magnetoelectric (TME) effect, has been predicted to induce exotic phenomena including the universal low-energy magneto-optical effects. Here we report the experimental demonstration of the long-sought TME effect, which is exemplified by magneto-optical Faraday and Kerr rotations in the quantum anomalous Hall (QAH) states of magnetic TI surfaces by terahertz magneto-optics. The universal relation composed of the observed Faraday and Kerr rotation angles but not of any material parameters (e.g. dielectric constant and magnetic susceptibility) well exhibits the trajectory toward the fine structure constant $\alpha$ $(= 2\pi e^2/hc \sim 1/137)$ in the quantized limit. Our result will pave a way for versatile TME effects with emergent topological functions.
