Viral infections remain a major risk in immunocompromised pediatric patients, and virus-specific T cell (VST) therapy has been successful for treatment of refractory viral infections in prior studies. We performed a phase II multicenter study (NCT03475212) for the treatment of pediatric patients with inborn errors of immunity and/or post allogeneic hematopoietic stem cell transplant with refractory viral infections using partially-HLA matched VSTs targeting cytomegalovirus, Epstein-Barr virus, or adenovirus. Primary endpoints were feasibility, safety, and clinical responses (>1 log reduction in viremia at 28 days). Secondary endpoints were reconstitution of antiviral immunity and persistence of the infused VSTs. Suitable VST products were identified for 75 of 77 clinical queries. Clinical responses were achieved in 29 of 47 (62%) of patients post-HSCT including 73% of patients evaluable at 1-month post-infusion, meeting the primary efficacy endpoint (>52%). Secondary graft rejection occurred in one child following VST infusion as described in a companion article. Corticosteroids, graft-versus-host disease, transplant-associated thrombotic microangiopathy, and eculizumab treatment correlated with poor response, while uptrending absolute lymphocyte and CD8 T cell counts correlated with good response. This study highlights key clinical factors that impact response to VSTs and demonstrates the feasibility and efficacy of this therapy in pediatric HSCT.