p-form electrodynamics as edge modes of a topological field theory

p-form electrodynamics in d ≥ 2 dimensions is shown to emerge as the edge modes of a topological field theory with a precise set of boundary conditions, through the Hamiltonian reduction of its action. Electric and magnetic charges correspond to Noether ones in the topological field theory. For chiral p-forms, the topological action can be consistently truncated, so that the Henneaux-Teitelboim action is recovered from a pure Chern-Simons theory, with a manifestly covariant stress-energy tensor at the boundary. Topologically massive p-form electrodynamics as well as axion couplings are also shown to be described through this mechanism by considering suitable (self-)interaction terms in the topological theory.