Despite the impressive improvements achieved by unsupervised deep neural networks in computer vision, natural language processing, and speech recognition tasks, such improvements have not generally been observed in ranking for information retrieval. The reason might be related to the complexity of the ranking problem, in the sense that it is not obvious how to learn from queries and documents when no supervised signal is available. Hence, in this paper, we propose to train a neural ranking model from a weak supervision signal, which is a training signal that can be obtained automatically without human labeling or any external resources (e.g., click data). To this aim, we use the output of a known unsupervised ranking model, such as BM25, as a weak supervision signal. We further train a set of simple yet effective ranking models based on feed-forward neural networks. We study their effectiveness under various learning scenarios (point-wise and pair-wise models) and using different input representations (i.e., from encoding query-document pairs into dense/sparse vectors to using word embedding representation). We train our network on 5 million unique queries obtained from the publicly available AOL query logs and two standard collections: a homogeneous news collection (Robust) and a heterogeneous large-scale web collection (ClueWeb). Our experiments indicate that feeding raw data to the networks and letting them learn representations for the input data leads to an impressive performance, with over 13% and 35% MAP improvements compared to the BM25 model on the Robust and the ClueWeb collections, respectively. Our findings suggest that neural ranking models can greatly benefit from large amounts of weakly labeled data that can be easily obtained from unsupervised IR models.