A Lagrangian approach has been used to derive gauge-origin independent expressions for two properties that rationalize magneto-optical activity, namely the Verdet constant V(ω) of the Faraday effect and the ℬ term of magnetic circular dichroism. The approach is expressed in terms of an atomic-orbital density-matrix based formulation of response theory and use London atomic orbitals to parametrize the magnetic field dependence. It yields a computational procedure which is both gauge-origin independent and suitable for linear-scaling at the level of time-dependent Hartree-Fock and density functional theory. The formulation includes a modified preconditioned conjugated gradient algorithm, which projects out the excited state component from the solution to the linear response equation. This is required when solving one of the response equations for the determination of the ℬ term and divergence is encountered if this component is not projected out. Illustrative results are reported for the Verdet constant of H2, HF, CO, N2O, and CH3CH2CH3 and for the ℬ term of pyrimidine, phosphabenzene, and pyridine. The results are benchmarked against gauge-origin independent CCSD values.