We present a nanodosimetric model for predicting the yield of double strand breaks (DSBs) and non-DSB clustered damages induced in irradiated DNA. The model uses experimental ionization cluster size distributions measured in a gas model by an ion counting nanodosimeter or, alternatively, distributions simulated by a Monte Carlo track structure code developed to simulate the nanodosimeter. The model is based on a straightforward combinatorial approach translating ionizations, as measured or simulated in a sensitive gas volume, to lesions in a DNA segment of one-two helical turns considered equivalent to the sensitive volume of the nanodosimeter. The two model parameters, corresponding to the probability that a single ion detected by the nanodosimeter corresponds to a single strand break or a single lesion (strand break or base damage) in the equivalent DNA segment, were tuned by fitting the model-predicted yields to previously measured double-strand break and double-strand lesion yields in plasmid DNA irradiated with protons and helium nuclei. Model predictions were also compared to both yield data simulated by the PARTRAC code for protons of a wide range of different energies and experimental DSB and non-DSB clustered DNA damage yield data from the literature. The applicability and limitations of this model in predicting the LET dependence of clustered DNA damage yields are discussed.