This paper describes the AC-coupled, single-sided, p-in-n silicon microstrip sensors used in the SemiConductor Tracker (SCT) of the ATLAS experiment at the CERN Large Hadron Collider (LHC). The sensor requirements, specifications and designs are discussed, together with the qualification and quality assurance procedures adopted for their production. The measured sensor performance is presented, both initially and after irradiation to the fluence anticipated after 10 years of LHC operation. The sensors are now successfully assembled within the detecting modules of the SCT, and the SCT tracker is completed and integrated within the ATLAS Inner Detector. Hamamatsu Photonics Ltd supplied 92.2% of the 15,392 installed sensors, with the remainder supplied by CiS.