Poincaré invariance in the ADM Hamiltonian approach to the general relativistic two-body problem

A previously found momentum-dependent regularization ambiguity in the third post-Newtonian two point-mass Arnowitt-Deser-Misner Hamiltonian is shown to be uniquely determined by requiring global Poincar\'e invariance. The phase-space generators realizing the Poincar\'e algebra are explicitly constructed.