Cyber attacks are growing in frequency and severity. Over the past year alone we have witnessed massive data breaches that stole personal information of millions of people and wide-scale ransomware attacks that paralyzed critical infrastructure of several countries. Combating the rising cyber threat calls for a multi-pronged strategy, which includes predicting when these attacks will occur. The intuition driving our approach is this: during the planning and preparation stages, hackers leave digital traces of their activities on both the surface web and dark web in the form of discussions on platforms like hacker forums, social media, blogs and the like. These data provide predictive signals that allow anticipating cyber attacks. In this paper, we describe machine learning techniques based on deep neural networks and autoregressive time series models that leverage external signals from publicly available Web sources to forecast cyber attacks. Performance of our framework across ground truth data over real-world forecasting tasks shows that our methods yield a significant lift or increase of F1 for the top signals on predicted cyber attacks. Our results suggest that, when deployed, our system will be able to provide an effective line of defense against various types of targeted cyber attacks.