In this work, we propose the use of Siamese Neural Networks to help solve the off-line handwritten signature verification problem with random forgeries in a writer-independent context. Our proposed solution can be used on new signers without the need for any additional training. Also, we have analyzed three types of synthetic data to increase the amount of samples and the variability needed for training deep neural networks: augmented data samples from GAVAB dataset, a proposal of compositional synthetic signature generation from shape primitives and the GPDSSynthetic dataset. The first two approaches are “on-demand” generators and they can be used during the training stage to produce a potentially infinite number of synthetic signatures. In our approach, we initially trained Siamese Neural Networks using signatures from GAVAB dataset and different combinations of synthetic data. The best verification results were obtained when combining original and synthetic signatures for training. Additionally, we tested our approach on the GPSSynthetic, MCYT, SigComp11 and CEDAR datasets demonstrating the generalization capabilities of our proposal.