The impact of axionlike particles (ALPs) on the search of permanent electric dipole moments (EDMs) of molecules, atoms, nuclei and nucleons is systematically investigated. Assuming the most general ALP effective field theory containing operators up to dimension-five, we evaluate the leading short-distance effects to the EDMs at two-loop order. The high sensitivity of EDMs to CP-violating ALP interactions is emphasized exploiting both the current and projected experimental sensitivities.