T cells engineered to express antigen-specific T cell receptors (TCRs) are potent therapies for viral infections and cancer. However, efficient identification of clinical candidate TCRs is complicated by the size and complexity of T cell repertoires and the challenges of working with primary T cells. Here we present a high-throughput method to identify TCRs with high functional avidity from diverse human T cell repertoires. The approach used massively parallel microfluidics to generate libraries of natively paired, full-length TCRαβ clones, from millions of primary T cells, which were then expressed in Jurkat cells. The TCRαβ–Jurkat libraries enabled repeated screening and panning for antigen-reactive TCRs using peptide major histocompatibility complex binding and cellular activation. We captured more than 2.9 million natively paired TCRαβ clonotypes from six healthy human donors and identified rare (<0.001% frequency) viral-antigen-reactive TCRs. We also mined a tumor-infiltrating lymphocyte sample from a patient with melanoma and identified several tumor-specific TCRs, which, after expression in primary T cells, led to tumor cell killing.