Chronic pain determines a substantial burden on individuals, employers, healthcare systems, and society. Most of the affected patients report dissatisfaction with currently available treatments. There are only a few and poor therapeutic options—some therapeutic agents are an outgrowth of drugs targeting acute pain, while others have several serious side effects. One of the primary degradative enzymes for endocannabinoids, fatty acid amide hydrolase (FAAH) attracted attention as a significant molecular target for developing new therapies for neuropsychiatric and neurological diseases, including chronic pain. Using chemical graph mining, quantitative structure–activity relationship (QSAR) modeling, and molecular docking techniques we developed a multi-step screening protocol to identify repurposable drugs as FAAH inhibitors. After screening the DrugBank database using our protocol, 273 structures were selected, with five already approved drugs, montelukast, repaglinide, revefenacin, raloxifene, and buclizine emerging as the most promising repurposable agents for treating chronic pain. Molecular docking studies indicated that the selected compounds interact with the enzyme mostly non-covalently (except for revefenacin) through shape complementarity to the large substrate-binding pocket in the active site. A molecular dynamics simulation was employed for montelukast and revealed stable interactions with the enzyme. The biological activity of the selected compounds should be further confirmed by employing in vitro and in vivo studies.