Recommender systems have shown to be a successful representative of how data availability can ease our everyday digital life.However, data privacy is one of the most prominent concerns in the digital era. After several data breaches and privacy scandals, the users are now worried about sharing their data. In the last decade, Federated Learning has emerged as a new privacy-preserving distributed machine learning paradigm. It works by processing data on the user device without collecting data in a central repository.In this paper, we present FedeRank, a federated recommendation algorithm. The system learns a personal factorization model onto every device. The training of the global model is modeled as a synchronous process between the central server and the federated clients.FedeRank takes care of computing recommendations in a distributed fashion and allows users to control the portion and type of data they want to share.By comparing with state-of-the-art centralized algorithms, extensive experiments show the effectiveness of FedeRank in terms of recommendation accuracy, even with a small portion of shared user data.Further analysis of the recommendation lists' diversity and novelty guarantees the suitability of the algorithm in real production environments.