A fully gauge-invariant (pseudoscalar) meson photoproduction amplitude off a nucleon including the final-state interaction is derived. The approach based on a comprehensive field-theoretical formalism developed earlier by one of the authors replaces certain dynamical features of the full interaction current by phenomenological auxiliary contact currents. A procedure is outlined that allows for a systematic improvement of this approximation. The feasibility of the approach is illustrated by applying it to both the neutral and charged pion photoproductions.