Change-point detection problems can be solved either by variational approaches based on total variation or by Bayesian procedures. The former class leads to small computational time but requires the choice of a regularization parameter that significantly impacts the achieved solution and whose automated selection remains a challenging problem. Bayesian strategies avoid this regularization parameter selection, at the price of high computational costs. In this contribution, we propose a hybrid Bayesian variational procedure that relies on the use of a hierarchical Bayesian model while preserving the computational efficiency of total variation optimization procedures. Behavior and performance of the proposed method compare favorably against those of a fully Bayesian approach, both in terms of accuracy and of computational time. Additionally, estimation performance are compared to the Stein unbiased risk estimate, for which the knowledge of the noise variance is needed.