A nonlocal current density which is a gauge invariant functional of the electron density in the absence of the magnetic field is constructed. Unlike local functionals, which reduce to the Thomas-Fermi current density in the limit of zero gradients, the new functional treats diamagnetism exactly. Additionally, unlike earlier local functionals, the new functional has the capacity to support net paramagnetism. The full magnetic susceptibility and chemical shielding tensor density functionals are also derived.