In the advent of a pervasive presence of location sharing services researchers gained an unprecedented access to the direct records of human activity in space and time. This paper analyses geo-located Twitter messages in order to uncover global patterns of human mobility. Based on a dataset of almost a billion tweets recorded in 2012 we estimate volumes of international travelers in respect to their country of residence. We examine mobility profiles of different nations looking at the characteristics such as mobility rate, radius of gyration, diversity of destinations and a balance of the inflows and outflows. The temporal patterns disclose the universal seasons of increased international mobility and the peculiar national nature of overseen travels. Our analysis of the community structure of the Twitter mobility network, obtained with the iterative network partitioning, reveals spatially cohesive regions that follow the regional division of the world. Finally, we validate our result with the global tourism statistics and mobility models provided by other authors, and argue that Twitter is a viable source to understand and quantify global mobility patterns.