We present the first complete (i.e., ambiguity-free) derivation of the equations of motion of two nonspinning compact objects up to the 4PN order, based on the Fokker action of point particles in harmonic coordinates. The last ambiguity parameter is determined from first principle, by resorting to a matching between the near zone and far zone fields, and a consistent computation of the 4PN tail effect in d dimensions. Dimensional regularization is used throughout for treating IR divergences appearing at 4PN order, as well as UV divergences due to the modeling of the compact objects as point particles.