Recently, Twitter has become the social network of choice for sharing and spreading information to a multitude of users through posts called 'tweets'. Users can easily re-share these posts to other users through 'retweets', which allow information to cascade to many more users, increasing its outreach. Clearly, being able to know the extent to which a post can be retweeted has great value in advertising, influencing and other such campaigns. In this paper we propose ViralBERT, which can be used to predict the virality of tweets using content- and user-based features. We employ a method of concatenating numerical features such as hashtags and follower numbers to tweet text, and utilise two BERT modules: one for semantic representation of the combined text and numerical features, and another module purely for sentiment analysis of text, as both the information within text and it's ability to elicit an emotional response play a part in retweet proneness. We collect a dataset of 330k tweets to train ViralBERT and validate the efficacy of our model using baselines from current studies in this field. Our experiments show that our approach outperforms these baselines, with a 13% increase in both F1 Score and Accuracy compared to the best performing baseline method. We then undergo an ablation study to investigate the importance of chosen features, finding that text sentiment and follower counts, and to a lesser extent mentions and following counts, are the strongest features for the model, and that hashtag counts are detrimental to the model.