T cells differentiate into functionally distinct subsets in response to pathogens, yet essential immune functions such as self-renewal, expansion, cytokine production, and cytotoxicity are common to multiple subsets and therefore must be programmed via shared regulatory mechanisms. To uncover these "archetypal" epigenomic programs, we integrated a single-cell multiomic (scATAC+RNA-seq) dataset of CD4 and CD8 T cells responding to acute and chronic viral infection with a comprehensive bulk ATAC-seq compendium. Our analysis reveals a modular architecture governing T cell identity, implicating distinct transcription factors in reusing regulatory programs across subsets and lineages. Notably, translationally important progenitor CD8 T cells, critical for sustained immunity and present in both acute and chronic infection, exhibit a composite regulatory state, combining a CD8 exhaustion program with a follicular helper CD4 T cell program. In sum, this resource and generalizable computational framework will aid the mechanistic dissection of adaptive immunity and immunotherapy design.