The pandemic caused by SARS-CoV-2 is still a major health problem. Newly emerging variants and long-COVID-19 represent a challenge for the global health system. In particular, individuals in developing countries with insufficient health care need easily accessible, affordable and effective treatments of COVID-19. Previous studies have demonstrated the efficacy of functional inhibitors of acid sphingomyelinase against infections with various viruses, including early variants of SARS-CoV-2. This work investigated whether the acid sphingomyelinase inhibitors fluoxetine and sertraline, usually used as antidepressant molecules in clinical practice, can inhibit the replication of the former and recently emerged SARS-CoV-2 variants in vitro. Fluoxetine and sertraline potently inhibited the infection with pseudotyped virus-like particles and SARS-CoV-2 variants D614G, alpha, delta, omicron BA.1 and omicron BA.5. These results highlight fluoxetine and sertraline as priority candidates for large-scale phase 3 clinical trials at different stages of SARS-CoV-2 infections, either alone or in combination with other medications.