The Hamiltonian formulation of the guiding centre drift orbits for three-dimensional (3D) toroidal configurations with general time-dependent electric and magnetic field structures has been extended to cover relativistic particles. For static 3D magnetic fields with nested magnetic surfaces, a mapping procedure from the equilibrium to the canonical coordinates is outlined. This transformation is shown to be so complicated that it renders impractical most applications in canonical coordinates. For magnetic coordinates, the transformation is straightforward. The relativistic guiding centre drift equations are explicitly derived with a constrained perturbed magnetic field that allows these coordinates to adopt a canonical structure.