We first present a method to compute the electro-optic tensor from first principles, explicitly taking into account the electronic, ionic and piezoelectric contributions. We then study the nonlinear optic behavior of three paradigmatic ferroelectric oxides. Our calculations reveal the dominant contribution of the soft mode to the electro-optic coefficients in LiNbO3 and BaTiO3 and its minor role in PbTiO3. We identify the coupling between the electric field and the polar atomic displacements along the B-O chains as the origin of the large electro-optic response in perovskite ABO3 compounds.