It is shown that the Standard Model (SM) admits a natural embedding in Weyl conformal geometry, which is truly minimal i.e. with no new fields beyond the SM spectrum and Weyl geometry. This is a gauge theory of scale invariance, with this symmetry inherited from the underlying geometry. This symmetry is spontaneously broken (Stueckelberg mechanism), so Einstein gravity is recovered in the broken phase, with a positive cosmological constant. We then examine some phenomenological implications.