We present a theory for the binding energy of clusters of polar molecules (ammonia or water) and an alkali metal atom (Na, Cs). The metal atom dissociates into a positive ion and a separate valence electron, which has the role of an excess electron. The positive ion and the electron have strong electromagnetic interactions with the molecules of the cluster. It is shown that the resulting polarization energy contains important many-body terms and that it is not possible to use a pair-potential approximation for the electronic potential. We propose a model for the ionization potential, including both-initial and final state effects. Our results for the ionization potential of metal-ammonia clusters agree well with recent experiments, indicating that a size-dependent transition from a single-center structure of small clusters to a fully solvated two-center structure for large clusters occurs. Spherically symmetric model structures do not yield a good agreement with experimental results for Na(H 2O) n clusters. Thus these clusters either have a distinct asymmetric shape because of strong hydrogen bridge bonding or an autoionizing resonance might have been observed in the experiment instead of the true ionization threshold.