Organ infiltration by donor T cells is critical to the development of acute graft-versus-host disease (aGVHD) in recipients after allogeneic hematopoietic stem cell transplant (allo-HCT). However, deconvoluting the transcriptional programs of newly recruited donor T cells from those of tissue-resident T cells in aGVHD target organs remains a challenge. Here, we combined the serial intravascular staining technique with single-cell RNA sequencing to dissect the tightly connected processes by which donor T cells initially infiltrate tissues and then establish a pathogenic tissue residency program in a rhesus macaque allo-HCT model that develops aGVHD. Our results enabled creation of a spatiotemporal map of the transcriptional programs controlling donor CD8⁺ T cell infiltration into the primary aGVHD target organ, the gastrointestinal (GI) tract. We identified the large and small intestines as the only two sites demonstrating allo-specific, rather than lymphodepletion-driven, T cell infiltration. GI-infiltrating donor CD8⁺ T cells demonstrated a highly activated, cytotoxic phenotype while simultaneously developing a canonical tissue-resident memory T cell (T_RM) transcriptional signature driven by interleukin-15 (IL-15)/IL-21 signaling. We found expression of a cluster of genes directly associated with tissue invasiveness, including those encoding adhesion molecules (ITGB2), specific chemokines (CCL3 and CCL4L1) and chemokine receptors (CD74), as well as multiple cytoskeletal proteins. This tissue invasion transcriptional signature was validated by its ability to discriminate the CD8⁺ T cell transcriptome of patients with GI aGVHD from those of GVHD-free patients. These results provide insights into the mechanisms controlling tissue occupancy of target organs by pathogenic donor CD8⁺ T_RM cells during aGVHD in primate transplant recipients.