American trypanosomiasis or Chagas disease, caused by Trypanosoma cruzi (T. cruzi), affects approximately 6–7 million people worldwide. However, its pharmacological treatment causes several uncomfortable side effects, causing patients’ treatment abandonment. Therefore, there is a need for new and better treatments. In this work, the molecular docking of nine hundred twenty-four FDA-approved drugs on three different sites of trypanothione reductase of T. cruzi (TcTR) was carried out to find potential trypanocidal agents. Finally, biological evaluations in vitro and in vivo were conducted with the selected FDA-approved drugs. Digoxin, alendronate, flucytosine, and dihydroergotamine showed better trypanocidal activity than the reference drugs benznidazole and nifurtimox in the in vitro evaluation against the trypomastigotes form. Further, these FDA-approved drugs were able to reduce 20–50% parasitemia in a short time in an in vivo model, although with less efficiency than benznidazole. Therefore, the results suggest a combined therapy of repurposed and canonical drugs against T. cruzi infection.