Background: Despite revised guidelines that no longer exclude people who inject drugs (PWID) from treatment for hepatitis C virus (HCV) infection, many clinicians are reluctant to treat recent PWID. This study aimed to evaluate the efficacy of sofosbuvir and velpatasvir therapy in people with chronic HCV infection and recent injection drug use. Methods: In this open-label, single-arm phase 4 trial (SIMPLIFY), we recruited participants with recent injection drug use (past 6 months) and chronic HCV genotype 1–6 infection from seven countries (19 sites). Participants received oral sofosbuvir (400 mg) and velpatasvir (100 mg) once daily for 12 weeks. Therapy was given in 1-week electronic blister packs to record the time and date of each dose. The primary endpoint was the proportion of patients with sustained virological response 12 weeks after completion of treatment (SVR12; defined as HCV RNA <12 IU/mL), analysed in all patients who received at least one dose. This study is registered with ClinicalTrials.gov, number NCT02336139, and follow-up is ongoing to evaluate the secondary endpoint of HCV reinfection. Findings: Between March 29, and Oct 31, 2016, we enrolled 103 participants; 29 (28%) of whom were female, nine (9%) had cirrhosis, 36 (35%) had HCV genotype 1, five (5%) had genotype 2, 60 (58%) had genotype 3, and two (2%) had genotype 4. 61 (59%) participants were receiving opioid substitution therapy during the study, 76 (74%) injected in the past month, and 27 (26%) injected at least daily in the past month. 100 (97%) of 103 participants completed treatment; two people were lost to follow-up and one person died from an overdose. There were no virological failures. 97 (94%, 95% CI 88–98) of 103 people achieved SVR12. Three participants with an end-of-treatment response did not have a SVR; two were lost to follow-up and one had reinfection. Drug use before and during treatment did not affect SVR12. Treatment-related adverse events were seen in 48 (47%) patients (one grade 3, no grade 4). Seven (7%) patients had at least one serious adverse event; only one such event (rhabdomyolysis, resolved) was possibly related to the therapy. One case of HCV reinfection was observed. Interpretation: HCV treatment should be offered to PWID, irrespective of ongoing drug use. Recent injection drug use should not be used as a reason to withhold reimbursement of HCV therapy. Funding: Gilead Sciences.