The ATLAS detector at CERN's Large Hadron Collider (LHC) will be exposed to proton-proton collisions from beams crossing at 40 MHz. A three-level trigger system will select potentially interesting events in order to reduce this rate to 100-200 Hz. A trigger decision is made by the Level-1 Central Trigger Processor (CTP) reducing the incoming rate to less than 100 kHz. The Level-1 decision is based on Calorimeter information and hits in dedicated Muon Trigger detectors. The final Level-1 trigger system is currently being installed in the experiment with completion expected in autumn 2007. Cosmic ray data are regularly recorded as an increasing fraction of the trigger system comes online. We present an overview of the Level-1 trigger system architecture and report on the installation and commissioning process at the ATLAS experimental site. Emphasis is put on the integration of the CTP with the Calorimeter and Muon Trigger systems. We show results from analyses of cosmic ray data recorded in situ and verify, where possible, that the Level-1 trigger meets the requirements and will be ready for data taking.