The ATLAS SemiConductor Tracker (SCT) was built in three sections: a barrel and two end-caps. This paper describes the design, construction and final integration of the barrel section. The barrel is constructed around four nested cylinders that provide a stable and accurate support structure for the 2112 silicon modules and their associated services. The emphasis of this paper is directed at the aspects of engineering design that turned a concept into a fully-functioning detector, as well as the integration and testing of large sub-sections of the final SCT barrel detector. The paper follows the chronology of the construction. The main steps of the assembly are described with the results of intermediate tests. The barrel service components were developed and fabricated in parallel so that a flow of detector modules, cooling loops, opto-harnesses and Frequency-Scanning-Interferometry (FSI) alignment structures could be assembled onto the four cylinders. Once finished, each cylinder was conveyed to the next site for the mounting of modules to form a complete single barrel. Extensive electrical and thermal function tests were carried out on the completed single barrels. In the next stage, the four single barrels and thermal enclosures were combined into the complete SCT barrel detector so that it could be integrated with the Transition Radiation Tracker (TRT) barrel to form the central part of the ATLAS inner detector. Finally, the completed SCT barrel was tested together with the TRT barrel in noise tests and using cosmic rays.