This article proposes FedPos, a federated transfer learning framework together with a novel position estimation method for Wi-Fi indoor positioning. Compared with traditional machine learning with privacy leakage problems and the cloud model trained through federated learning (FL) fails in personalization, the FedPos framework aggregates nonclassification layer parameters of models trained from different environments to build a robust and versatile encoder on the cloud server while preserving user privacy. The global cloud encoder can aggregate different classifiers and then construct personalized models for new users through fine-tuning. The proposed framework can be updated incrementally and is highly extensible. Specifically, we exploit channel state information (CSI) as the positioning feature and assess the transferability of a lightweight convolutional neural network (CNN) in unfamiliar environments. We evaluate the performance of our proposed framework and position estimation method in different indoor environments. Our experimental results indicate that the proposed framework can achieve a mean localization error of 42.18 cm in a 64-position living room. They also confirm that FedPos can achieve a 5.22% average localization performance boost and reduce the average model training time by about 34.78% when compared with normal training. By reusing part of the feature extractor layers that are trained from other environments, at least 65% of training data can be saved to achieve a localization performance that is similar to the base model. Overall, the proposed position estimation method can effectively improve localization accuracy as compared with seven other existing CSI-based methods.