Biometric systems have been used in a wide range of applications. In this paper, we have introduced an online signature verification system using deep neural network models. The proposed system is designed to be used in a production environment and has accuracies on par with the state-of-the-art signature verification methods. It authenticates much faster than most of the existing signature verification systems (less than 2 seconds). To achieve better accuracies and faster training times, a feature vector with 42 features, both static and dynamic, is obtained from the signature sample. This feature vector is fed into the user identification model, which predicts the identity of the user with about 99% accuracy and based on this prediction, the user authentication model predicts if the signature is genuine or forged for that recognized user, with about 98% accuracy. The best possible accuracy achieved by the proposed system for 40 users is 97.5% and EER about 2%. The dataset from the Signature Verification Competition 2004 (SVC2004) was used to assess the performance of the proposed system. The results show that the proposed system competes with and even outperforms existing methods.