Deep Learning-based computational pathology algorithms have demonstrated profound ability to excel in a wide array of tasks that range from characterization of well known morphological phenotypes to predicting non human-identifiable features from histology such as molecular alterations. However, the development of robust, adaptable and accurate deep learning-based models often rely on the collection and time-costly curation large high-quality annotated training data that should ideally come from diverse sources and patient populations to cater for the heterogeneity that exists in such datasets. Multi-centric and collaborative integration of medical data across multiple institutions can naturally help overcome this challenge and boost the model performance but is limited by privacy concerns among other difficulties that may arise in the complex data sharing process as models scale towards using hundreds of thousands of gigapixel whole slide images. In this paper, we introduce privacy-preserving federated learning for gigapixel whole slide images in computational pathology using weakly-supervised attention multiple instance learning and differential privacy. We evaluated our approach on two different diagnostic problems using thousands of histology whole slide images with only slide-level labels. Additionally, we present a weakly-supervised learning framework for survival prediction and patient stratification from whole slide images and demonstrate its effectiveness in a federated setting. Our results show that using federated learning, we can effectively develop accurate weakly-supervised deep learning models from distributed data silos without direct data sharing and its associated complexities, while also preserving differential privacy using randomized noise generation.