The Swift Gamma-Ray Burst Explorer is designed to make prompt multi-wavelength observations of Gamma-Ray Bursts and GRB afterglows. The X-ray Telescope enables Swift to determine GRB positions with a few arcseconds accuracy within 100 seconds of the burst onset. The XRT utilizes a mirror set built for JET-X and an XMM-Newton/EPIC MOS CCD detector to provide a sensitive broad-band (0.2-10 keV) X-ray imager with an effective area of more than 120 cm2 at 1.5 keV, a field of view of 23.6 × 23.6 arcminutes, and an angular resolution of 18 arcseconds (HPD). The detection sensitivity is 2×10-14 erg cm-2 s-1 in 104 seconds. The instrument provides automated source detection and position reporting within 5 seconds of target acquisition. It can also measure the redshifts of GRBs with Iron line emission or other spectral features. The XRT operates in an auto-exposure mode, adjusting the CCD readout mode automatically to optimize the science return as the source intensity fades. The XRT measures spectra and lightcurves of the GRB afterglow beginning about a minute after the burst and follows each burst for days or weeks. We provide an overview of the X-ray Telescope scientific background from which the systems engineering requirements were derived, with specific emphasis on the design and qualification aspects from conception through to launch. We describe the impact on cleanliness and vacuum requirements for the instrument low energy response and to maintain the high sensitivity to the fading signal of the Gamma-ray Bursts.