The ATLAS (A Toroidal LHC ApparatuS) Inner Detector provides charged particle tracking in the centre of the ATLAS experiment at the Large Hadron Collider (LHC). The Inner Detector consists of three subdetectors: the Pixel Detector, the Semiconductor Tracker (SCT), and the Transition Radiation Tracker (TRT). This paper summarizes the tests that were carried out at the final stage of SCT+TRT integration prior to their installation in ATLAS. The combined operation and performance of the SCT and TRT barrel and endcap detectors was investigated through a series of noise tests, and by recording the tracks of cosmic rays. This was a crucial test of hardware and software of the combined tracker detector systems. The results of noise and cross-talk tests on the SCT and TRT in their final assembled configuration, using final readout and supply hardware and software, are reported. The reconstruction and analysis of the recorded cosmic tracks allowed testing of the offline analysis chain and verification of basic tracker performance parameters, such as efficiency and spatial resolution, in combined operation before installation.