There is no treatment for the myelin loss in multiple sclerosis, ultimately resulting in the axonal degeneration that leads to the progressive phase of the disease. We established a multi-tiered platform for the sequential screening of drugs that could be repurposed as remyelinating agents. We screened a library of 2,000 compounds (mainly Food and Drug Administration (FDA)-approved compounds and natural products) for cellular metabolic activity on mouse oligodendrocyte precursors (OPC), identifying 42 molecules with significant stimulating effects. We then characterized the effects of these compounds on OPC proliferation and differentiation in mouse glial cultures, and on myelination and remyelination in organotypic cultures. Three molecules, edaravone, 5-methyl-7-methoxyisoflavone and lovastatin, gave positive results in all screening tiers. We validated the results by retesting independent stocks of the compounds, analyzing their purity, and performing dose-response curves. To identify the chemical features that may be modified to enhance the compounds' activity, we tested chemical analogs and identified, for edaravone, the functional groups that may be essential for its activity. Among the selected remyelinating candidates, edaravone appears to be of strong interest, also considering that this drug has been approved as a neuroprotective agent for acute ischemic stroke and amyotrophic lateral sclerosis in Japan.