Currently, when the existing magnetic dipole inversion methods are used, the classification process heavily relies on the localization results, and the localization error can significantly deteriorate the classification results. In order to address this problem, the present study proposes a novel magnetic dipole inversion method based on tensor geometric invariants, in which localization and classification processes are mutually independent. First, based on tensor geometric invariants, it was proved that the cross product between the intermediate eigenvectors at any two measurement points in the dipole magnetic field is either in the same direction as the magnetic moment vector or in the opposite direction. Accordingly, the direction of the magnetic moment vector could be directly obtained. Next, based on tensor geometric invariants, nonlinear equations including the position parameters of the dipole were constructed so as to derive the position of the dipole. By employing the proposed method, localization and classification were found to be two mutually independent processes, both of which are relatively insensitive to attitude changes of the measurement system. The present simulation results demonstrate that the proposed method is superior to the scalar triangulation and ranging (STAR) method, the Nara improved method, and the STAR improved method in both classification and localization performance. Moreover, the proposed method exhibits the strongest noise immunity and can be effectively used for real-time inversion.