We present a method for large-scale geo-localization and global tracking of mobile devices in urban outdoor environments. In contrast to existing methods, we instantaneously initialize and globally register a SLAM map by localizing the first keyframe with respect to widely available untextured 2.5D maps. Given a single image frame and a coarse sensor pose prior, our localization method estimates the absolute camera orientation from straight line segments and the translation by aligning the city map model with a semantic segmentation of the image. We use the resulting 6DOF pose, together with information inferred from the city map model, to reliably initialize and extend a 3D SLAM map in a global coordinate system, applying a model-supported SLAM mapping approach. We show the robustness and accuracy of our localization approach on a challenging dataset, and demonstrate unconstrained global SLAM mapping and tracking of arbitrary camera motion on several sequences.