We will define the multipole moments of the gravitational field (in an arbitrary metric theory of gravity) in terms of canonical Noether charges associated with specific residual transformations of the harmonic gauge, which we call multipole symmetries. This new definition exactly matches Thorne’s mass and current multipole moments in Einstein gravity, which are defined in terms of metric components. For radiative configurations, the total multipole charges – including the contributions from the source and the radiation – are given by surface charges at spatial infinity, while the source multipole moments are naturally identified by surface integrals in the near-zone. The conservation of total multipole charges is used to derive the variation of source multipole moments in terms of the radiative multipole fluxes.