Antibiotic-resistant bacterial pathogens are a very challenging problem nowadays. Helicobacter pylori is one of the most widespread and successful human pathogens since it colonizes half of the world population causing chronic and atrophic gastritis, peptic ulcer, mucosa-associated lymphoid tissue-lymphoma, and even gastric adenocarcinoma. Moreover, it displays resistance to numerous antibiotics. One of the H. pylori pivotal transcription factors, HP1043, plays a fundamental role in regulating essential cellular processes. Like other bacterial transcription factors, HP1043 does not display a eukaryote homolog. These characteristics make HP1043 a promising candidate to develop novel antibacterial strategies. Drug repositioning is a relatively recent strategy employed in drug development; testing approved drugs on new targets considerably reduces the time and cost of this process. The combined computational and in vitro approach further reduces the number of compounds to be tested in vivo. Our aim was to identify a subset of known drugs able to prevent HP1043 binding to DNA promoters. This result was reached through evaluation by molecular docking the binding capacity of about 14,350 molecules on the HP1043 dimer in both conformations, bound and unbound to the DNA. Employing an ad hoc pipeline including MMGBSA molecular dynamics, a selection of seven drugs was obtained. These were tested in vitro by electrophoretic mobility shift assay to evaluate the HP1043–DNA interaction. Among these, three returned promising results showing an appreciable reduction of the DNA-binding activity of HP1043. Overall, we applied a computational methodology coupled with experimental validation of the results to screen a large number of known drugs on one of the H. pylori essential transcription factors. This methodology allowed a rapid reduction of the number of drugs to be tested, and the drug repositioning approach considerably reduced the drug design costs. Identified drugs do not belong to the same pharmaceutical category and, by computational analysis, bound different cavities, but all display a reduction of HP1043 binding activity on the DNA.