The ability to recognise emotions lends a conversational artificial intelligence a human touch. While emotions in chit-chat dialogues have received substantial attention, emotions in task-oriented dialogues remain largely unaddressed. This is despite emotions and dialogue success having equally important roles in a natural system. Existing emotion-annotated task-oriented corpora are limited in size, label richness, and public availability, creating a bottleneck for downstream tasks. To lay a foundation for studies on emotions in task-oriented dialogues, we introduce EmoWOZ, a large-scale manually emotion-annotated corpus of task-oriented dialogues. EmoWOZ is based on MultiWOZ, a multi-domain task-oriented dialogue dataset. It contains more than 11K dialogues with more than 83K emotion annotations of user utterances. In addition to Wizard-of-Oz dialogues from MultiWOZ, we collect human-machine dialogues within the same set of domains to sufficiently cover the space of various emotions that can happen during the lifetime of a data-driven dialogue system. To the best of our knowledge, this is the first large-scale open-source corpus of its kind. We propose a novel emotion labelling scheme, which is tailored to task-oriented dialogues. We report a set of experimental results to show the usability of this corpus for emotion recognition and state tracking in task-oriented dialogues.