In this paper, we design an information-based multi-robot source seeking algorithm where a group of mobile sensors localizes and moves close to a single source using only local range-based measurements. In the algorithm, the mobile sensors perform source identification/localization to estimate the source location; meanwhile, they move to new locations to maximize the Fisher information about the source contained in the sensor measurements. In doing so, they improve the source location estimate and move closer to the source. Our algorithm is superior in convergence speed compared with traditional field climbing algorithms, is flexible in the measurement model and the choice of information metric, and is robust to measurement model errors. Moreover, we provide a fully distributed version of our algorithm, where each sensor decides its own actions and only shares information with its neighbors through a sparse communication network. We perform intensive simulation experiments to test our algorithms on large-scale systems and physical experiments on small ground vehicles with light sensors, demonstrating success in seeking a light source.