Given the historical movement trajectories of a set of individual human agents (e.g., pedestrians, taxi drivers) and a set of new trajectories claimed to be generated by a specific agent, the Human Mobility Signature Identification (HuMID) problem aims at validating if the incoming trajectories were indeed generated by the claimed agent. This problem is important in many real-world applications such as driver verification in ride-sharing services, risk analysis for auto insurance companies, and criminal identification. Prior work on identifying human mobility behaviors requires additional data from other sources besides the trajectories, e.g., sensor readings in the vehicle for driving behavior identification. However, these data might not be universally available and is costly to obtain. To deal with this challenge, in this work, we make the first attempt to match identities of human agents only from the observed location trajectory data by proposing a novel and efficient framework named Spatio-temporal Siamese Networks (ST-SiameseNet). For each human agent, we extract a set of profile and online features from his/her trajectories. We train ST-SiameseNet to predict the mobility signature similarity between each pair of agents, where each agent is represented by his/her trajectories and the extracted features. Experimental results on a real-world taxi trajectory dataset show that our proposed ST-SiamesNet can achieve an $F_1$ score of $0.8508$, which significantly outperforms the state-of-the-art techniques.