The Global Tracking Trigger (GTT) of the ZEUS experiment is described. The GTT is data driven at the ZEUS first level trigger rate of ≤ 600 Hz and performs event-based track finding on data from the experiment's Central Tracking Detector (CTD), silicon Micro Vertex Detector (MVD) and Straw Tube Tracker (STT) forward detectors. The resulting track-based trigger quantities calculated (track multiplicity, vertices, vector meson masses, background event probabilities, etc.) are available within ∼ 9 ms and are used in the experiment's second level trigger to improve the selection of physics events. Detector information is pushed to the PC farm of the GTT using PowerPC VME board computers which are either embedded within the detector's frontend readout system (MVD) or are parasitically attached to them via multiple serial transputer links (CTD and STT). Data flow and control is performed via point-to-point Fast and Giga ethernet switched network connections using the TCP protocol. The principal design challenges were: integrating new and interfacing to existing frontend systems, providing a useful trigger result, satisfying the rate and latency requirements and not interfering with ongoing data taking during commissioning. These aims have been achieved. The GTT has been actively used in the ZEUS trigger since 2004 when an initial CTD-only algorithm was used; in 2005 this was upgraded to use MVD information which significantly improves track and primary vertex resolutions. Commissioning problems delayed the STT implementation and its use in the GTT has only been tested.