Microblog classification has received a lot of attention in recent years. Different classification tasks have been investigated, most of them focusing on classifying microblogs into a small number of classes (five or less) using a training set of manually annotated tweets. Unfortunately, labelling data is tedious and expensive, and finding tweets that cover all the classes of interest is not always straightforward, especially when some of the classes do not frequently arise in practice. In this paper we study an approach to tweet classification based on distant supervision, whereby we automatically transfer labels from one social medium to another for a single-label multi-class classification task. In particular, we apply YouTube video classes to tweets linking to these videos. This provides for free a virtually unlimited number of labelled instances that can be used as training data. The classification experiments we have run show that training a tweet classifier via these automatically labelled data achieves substantially better performance than training the same classifier with a limited amount of manually labelled data; this is advantageous, given that the automatically labelled data come at no cost. Further investigation of our approach shows its robustness when applied with different numbers of classes and across different languages.