Topics discussed on social media platforms contain a disparate amount of information written in colloquial language, making it difficult to understand the narrative of the topic. In this paper, we take a step forward, towards the resolution of this problem by proposing a framework that performs the automatic extraction of narratives from a document, such as tweet posts. To this regard, we propose a methodology that extracts information from the texts through a pipeline of tasks, such as co-reference resolution and the extraction of entity relations. The result of this process is embedded into an annotation file to be used by subsequent operations, such as visualization schemas. We named this framework Tweet2Story and measured its effectiveness under an evaluation schema that involved three different aspects: (i) as an Open Information extraction (OpenIE) task, (ii) by comparing the narratives of manually annotated news articles linked to tweets about the same topic and (iii) by comparing their knowledge graphs, produced by the narratives, in a qualitative way. The results obtained show a high precision and a moderate recall, on par with other OpenIE state-of-the-art frameworks and confirm that the narratives can be extracted from small texts. Furthermore, we show that the narrative can be visualized in an easily understandable way.