We propose a new task, dataset and model for grounded video caption generation. This task unifies captioning and object grounding in video, where the objects in the caption are grounded in the video via temporally consistent bounding boxes. We introduce the following contributions. First, we present a task definition and a manually annotated test dataset for this task, referred to as GROunded Video Caption Generation (GROC). Second, we introduce a large-scale automatic annotation method leveraging an existing model for grounded still image captioning together with an LLM for summarising frame-level captions into temporally consistent captions in video. Furthermore, we prompt the LLM to track by language -- classifying noun phrases from the frame-level captions into noun phrases of the video-level generated caption. We apply this approach to videos from the HowTo100M dataset, which results in a new large-scale training dataset, called HowToGround, with automatically annotated captions and spatio-temporally consistent bounding boxes with coherent natural language labels. Third, we introduce a new grounded video caption generation model, called VideoGround, and train the model on the new automatically annotated HowToGround dataset. Finally, results of our VideoGround model set the state of the art for the new task of grounded video caption generation. We perform extensive ablations and demonstrate the importance of key technical contributions of our model.