The traditional cloud-centric approach for Deep Learning (DL) requires training data to be collected and processed at a central server which is often challenging in privacy-sensitive domains like healthcare. Towards this, a new learning paradigm called Federated Learning (FL) has been proposed that brings the potential of DL to these domains while addressing privacy and data ownership issues. FL enables clients to learn a shared ML model while keeping the data local. However, conventional FL systems face challenges such as scalability, complex infrastructure management, and wasted compute and incurred costs due to idle clients. These challenges of FL systems closely align with the core problems that serverless computing and Function-as-a-Service (FaaS) platforms aim to solve. These include rapid scalability, no infrastructure management, automatic scaling to zero for idle clients, and a pay-per-use billing model. To this end, we present a novel system and framework for serverless FL, called FedLess. Our system supports multiple commercial and self-hosted FaaS providers and can be deployed in the cloud, on-premise in institutional data centers, and on edge devices. To the best of our knowledge, we are the first to enable FL across a large fabric of heterogeneous FaaS providers while providing important features like security and Differential Privacy. We demonstrate with comprehensive experiments that the successful training of DNNs for different tasks across up to 200 client functions and more is easily possible using our system. Furthermore, we demonstrate the practical viability of our methodology by comparing it against a traditional FL system and show that it can be cheaper and more resource-efficient.