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The current trend of over-parameterized Deep Neural Networks makes the deployment on resource constrained systems challenging. To deal with this, optimization techniques, such as network pruning, can be adopted. We propose a novel pruning technique based on trainable probability masks that, when binarized, select the elements of the network to prune. Our method features i) an automatic selections of the elements to prune by jointly training the binary masks with the model, ii) the capability of controlling the pruning level through hyper-parameters of a novel regularization term. We assess the effectiveness of our method by employing it in the structured pruning of the fully connected layers of shallow and deep neural networks where it outperforms the magnitude-based pruning approaches.