Twitter provides an open and rich source of data for studying human behaviour at scale and is widely used in social and network sciences. However, a major criticism of Twitter data is that demographic information is largely absent. Enhancing Twitter data with user ages would advance our ability to study social network structures, information flows and the spread of contagions. Approaches toward age detection of Twitter users typically focus on specific properties of tweets, e.g., linguistic features, which are language dependent. In this paper, we devise a language-independent methodology for determining the age of Twitter users from data that is native to the Twitter ecosystem. The key idea is to use a Bayesian framework to generalise ground-truth age information from a few Twitter users to the entire network based on what/whom they follow. Our approach scales to inferring the age of 700 million Twitter accounts with high accuracy.