Estimating accurate radio maps is important for various tasks in wireless communications, such as channel modeling, resource allocation, and network planning, to name a few. Due to the changes in the propagation characteristics of the wireless environments, a radio map model learned under a particular wireless environment cannot be directly used in a new wireless environment. Moreover, learning a new model for every environment requires, in general, a large amount of data and is computationally demanding. In this work, we design an effective novel data-driven transfer learning method that transfers and fine-tunes a deep neural network (DNN)-based radio map model learned from an original wireless environment to other wireless environments with a certain level of similarity, allowing the radio map to be estimated with less amount of training data. As opposed to other widely used similarity measures that do not take into account the wireless propagation characteristics, we design a data-driven similarity measure that predicts the mean square error (MSE) and the amount of training data needed when learning a radio map in a new wireless environment. The proposed solution is corroborated by extensive simulations over a range of wireless environments, achieving savings of approximately 60-70% in sensor measurement data.