Graphene, a monolayer sheet of carbon atoms, exhibits intriguing electronic properties that arise from its massless Dirac dispersion of electrons. A striking example is the half-integer quantum Hall effect, which endorses the presence of Dirac cones or, equivalently, a non-zero (π) Berry's (topological) phase. It is curious how these anomalous features of Dirac electrons would affect optical properties. Here we observe the quantum magneto-optical Faraday and Kerr effects in graphene in the terahertz frequency range. Our results detect the quantum plateaus in the Faraday and Kerr rotations at precisely the quantum Hall steps that hallmark the Dirac electrons, with the rotation angle defined by the fine-structure constant. The robust quantum Hall plateaus in the optical regime, besides being conceptually interesting, may open avenues for new graphene-based optoelectronic applications.