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The dynamics and influence of fake news on Twitter during the 2016 US presidential election remains to be clarified. Here, we use a dataset of 171 million tweets in the five months preceding the election day to identify 30 million tweets, from 2.2 million users, which contain a link to news outlets. Based on a classification of news outlets curated by www.opensources.co, we find that 25% of these tweets spread either fake or extremely biased news. We characterize the networks of information flow to find the most influential spreaders of fake and traditional news and use causal modeling to uncover how fake news influenced the presidential election. We find that, while top influencers spreading traditional center and left leaning news largely influence the activity of Clinton supporters, this causality is reversed for the fake news: the activity of Trump supporters influences the dynamics of the top fake news spreaders.