We define multipole moments for an arbitrary theory of gravity in terms of canonical Noether charges associated with specific residual transformations in canonical harmonic gauge, which we call multipole symmetries. We show that our definition exactly matches Thorne's mass and current multipole moments in Einstein gravity. For radiative configurations, the total multipole charges -- including the contributions from the source and the radiation -- are given by surface charges at spatial infinity. The conservation of total multipole charges is used to derive the variation of source multipole...
