CD8+ T cells that respond to chronic viral infections or cancer are characterized by the expression of inhibitory receptors such as programmed cell death protein 1 (PD-1) and by the impaired production of cytokines. This state of restrained functionality—which is referred to as T cell exhaustion1,2—is maintained by precursors of exhausted T (TPEX) cells that express the transcription factor T cell factor 1 (TCF1), self-renew and give rise to TCF1− exhausted effector T cells3–6. Here we show that the long-term proliferative potential, multipotency and repopulation capacity of exhausted T cells during chronic infection are selectively preserved in a small population of transcriptionally distinct CD62L+ TPEX cells. The transcription factor MYB is not only essential for the development of CD62L+ TPEX cells and maintenance of the antiviral CD8+ T cell response, but also induces functional exhaustion and thereby prevents lethal immunopathology. Furthermore, the proliferative burst in response to PD-1 checkpoint inhibition originates exclusively from CD62L+ TPEX cells and depends on MYB. Our findings identify CD62L+ TPEX cells as a stem-like population that is central to the maintenance of long-term antiviral immunity and responsiveness to immunotherapy. Moreover, they show that MYB is a transcriptional orchestrator of two fundamental aspects of exhausted T cell responses: the downregulation of effector function and the long-term preservation of self-renewal capacity.