The wavelet detection algorithm (WDA) described in the accompanying paper by Lazzati et al. is suited to a fast and efficient analysis of images taken with the High-Resolution Imager (HRI) instrument on board the ROSAT satellite. An extensive testing is carried out on the detection pipeline: HRI fields with different exposure times are simulated and analyzed in the same fashion as the real data. Positions are recovered with errors of a few arcseconds, whereas fluxes are within a factor of 2 from their input values in more than 90% of the cases in the deepest images. Unlike the "sliding-box" detection algorithms, the WDA also provides a reliable description of the source extension, allowing for a complete search of, e.g., supernova remnants or clusters of galaxies in the HRI fields. A completeness analysis on simulated fields shows that for the deepest exposures considered (similar to 120 ks) a limiting flux of similar to 3 x 10(-15) ergs s(-1) cm(-2) can be reached over the entire field of view. We test the algorithm on real HRI fields selected for their crowding and/or the presence of extended or bright sources (e.g., clusters of galaxies and stars, supernova remnants). We show that our algorithm compares favorably with other X-ray detection algorithms, such as XIMAGE and EXSAS. analysis with the WDA of the large set of HRI data will allow us to survey similar to 400 deg(2) down to a limiting flux of similar to 10(-13) ergs s(-1) cm(-2), and similar to 0.3 deg(2) down to similar to 3 x 10(-15) ergs s(-1) cm(-2). A complete catalog will result from our analysis, consisting of the Brera Multiscale Wavelet Bright Source Catalog (BMW-BSC), with sources detected with a significance of greater than or similar to 4.5 sigma, and the Faint Source Catalog (BMW-FSC), with sources at greater than or similar to 3.5 sigma. A conservative estimate based on the extragalactic log N-log S indicates that at least 16,000 sources will be revealed in the complete analysis of the entire HRI data set.