For the conjugated oligomers of the type (M)(N) described by a tight-binding Hamiltonian with the nearest-neighbor interaction between monomers M of otherwise arbitrary electronic structure, the bridge-mediated donor-acceptor effective coupling is proved to be ruled by an exponential law T-DA(0) exp(-delta N). Previously, this kind of dependence has been recovered in many numerical treatments or guessed on phenomenological basis. The exact expressions of the decay constant delta and pre-exponential factor T-DA(0) obtained in terms of the monomer Green function provide, for the first time, an analytical relationship between the oligomer pi electronic structure and through-conjugated-bridge tunneling efficiency. For the fundamental band gap a simple analytical approximation of the effective coupling that relates delta to the model of through-rectangular-barrier tunneling is also given. The dependence of the effective coupling on energy of tunneling electron (hole) is examined in detail and illustrated for oligomers of polyenes, polyparaphenylenes, and polyheterocycles. The results obtained suggest a quick and reliable estimate of the effective coupling with a deep insight into the physical origins of related switching abilities of conjugated oligomers as a useful alternative to lengthy numerical calculations.