We present the catalogue of the REFLEX Cluster Survey providing information on the X-ray properties , redshifts , and some identification details of the clusters in the REFLEX sample . The catalogue describes a statistically complete X-ray flux-limited sample of 447 galaxy clusters above an X-ray flux of 3 10 ^ { -12 } erg s ^ { -1 } cm ^ { -2 } ( 0.1 to 2.4 keV ) in an area of 4.24 ster in the southern sky . The cluster candidates were first selected by their X-ray emission in the ROSAT-All Sky Survey and subsequently spectroscopically identified in the frame of an ESO key programme . Previously described tests have shown that the sample is more than 90 % complete and there is a conservative upper limit of 9 % on the fraction of clusters with a dominant X-ray contamination from AGN . In addition to the cluster catalogue we also describe the complete selection criteria as a function of the sky position and the conversion functions used to analyse the X-ray data . These are essential for the precise statistical analysis of the large-scale cluster distribution . This data set is at present the largest , statistically complete X-ray galaxy cluster sample . Together with these data set we also provide for the first time the full three-dimensional selection function . The sample forms the basis of several cosmological studies , one of the most important applications being the assessment of the statistics of the large-scale structure of the universe and the test of cosmological models . Part of these cosmological results have already been published . The full versions of Tables 2 through 9 will be available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr ( 130.79.128.5 ) or via http : //cdsweb.u-strasbg.fr/cgi-bin/qcat ? J/A+A/ as well as on our home page http : //www.xray.mpe.mpg.de/theorie/REFLEX/DATA