Four-component relativistic treatments of the electron paramagnetic resonance g-tensor have so far been based on a common gauge origin and a restricted kinetically balanced basis. The results of such calculations are prone to exhibit a dependence on the choice of the gauge origin for the vector potential associated with uniform magnetic field and a related dependence on the basis set quality. In this work, this gauge problem is addressed by a distributed-origin scheme based on the London atomic orbitals, also called gauge-including atomic orbitals (GIAOs), which have proven to be a practical approach for calculations of other magnetic properties. Furthermore, in the four-component relativistic domain, it has previously been shown that a restricted magnetically balanced (RMB) basis for the small component of the four-component wavefunctions is necessary for achieving robust convergence with regard to the basis set size. We present the implementation of a four-component density functional theory (DFT) method for calculating the g-tensor, incorporating both the GIAOs and RMB basis and based on the Dirac-Coulomb Hamiltonian. The approach utilizes the state-of-the-art noncollinear Kramers-unrestricted DFT methodology to achieve rotationally invariant results and inclusion of spin-polarization effects in the calculation. We also show that the gauge dependence of the results obtained is connected to the nonvanishing integral of the current density in a finite basis, explain why the results of cluster calculations exhibit surprisingly low gauge dependence, and demonstrate that the gauge problem disappears for systems with certain point-group symmetries.