Remdesivir was the first antiviral approved for treating COVID-19. We investigated its patterns of use, effectiveness and safety in clinical practice in Greece. This is a retrospective observational study of hospitalized adults who received remdesivir for COVID-19 in September 2020–February 2021. The main endpoints were the time to recovery (hospital discharge within 30 days from admission) and safety. The “early” (remdesivir initiation within 24 h since hospitalization) and “deferred” (remdesivir initiation later on) groups were compared. One thousand and four patients (60.6% male, mean age 61 years, 74.3% with severe disease, 70.9% with ≥1 comorbidities) were included, and 75.9% of them were on a 5-day regimen, and 86.8% were in the early group. Among those with a baseline mild/moderate disease, the median (95% CI) time to recovery was 8 (7–9) and 12 (11–14) days for the early and deferred groups, respectively (p < 0.001). The corresponding estimates for those with a severe disease were 10 (9–10) and 13 (11–15) days, respectively (p = 0.028). After remdesivir initiation, increased serum transaminases and an acute kidney injury were observed in 6.9% and 2.1%, respectively. Nine (0.9%) patients discontinued the treatment due to adverse events. The effectiveness of remdesivir was increased when it was taken within 24 h since admission regardless of the disease severity. Remdesivir’s safety profile is similar to that described in clinical trials and other real-world cohorts.