In this work we present a novel generative approach for the score-level fusion of speaker verification systems. The proposed method employs a copula-based representation of the joint score distribution of multiple speaker recognizers that allows decoupling the dependency structure from the characterization of the marginal densities of the scores of different systems. This allows us to combine complex Variance-Gamma marginals with a simple Gaussian copula to obtain a characterization of the joint target and non-target score distribution that can be effectively employed for the score-level combination of multiple recognizers. Our results on NIST SRE 2019 and SITW datasets show that our approach is competitive with respect to state-of-the-art discriminative score fusion techniques, providing both accurate and well-calibrated scores, with a measured Cllr reduction of up to 7% relative with respect to discriminative linear fusion methods.