Late embryogenesis abundant (LEA) proteins are identified in many crops for their response and role in adaptation to various abiotic stresses, such as drought, salinity, and temperature. The LEA genes have been studied systematically in several crops but not in Vigna crops. In this study, we reported the first comprehensive analysis of the LEA gene family in three legume species, namely, mung bean (Vigna radiata), adzuki bean (Vigna angularis), and cowpea (Vigna unguiculata), and the cross-species expression of VrLEA genes in a wild tetraploid species, Vigna glabrescens. A total of 201 LEA genes from three Vigna crops were identified harboring the LEA conserved motif. Among these 55, 64, and 82 LEA genes were identified in mung bean, adzuki bean, and cowpea genomes, respectively. These LEA genes were grouped into eight different classes. Our analysis revealed that the cowpea genome comprised all eight classes of LEA genes, whereas the LEA-6 class was absent in the mung bean genome. Similarly, LEA-5 and LEA-6 were absent in the adzuki bean genome. The analysis of LEA genes provides an insight into their structural and functional diversity in the Vigna genome. The genes, such as VrLEA-2, VrLEA-40, VrLEA-47, and VrLEA-55, were significantly upregulated in the heat-tolerant genotype under stress conditions indicating the basis of heat tolerance. The successful amplification and expression of VrLEA genes in V. glabrescens indicated the utility of the developed markers in mung bean improvement. The results of this study increase our understanding of LEA genes and provide robust candidate genes for future functional investigations and a basis for improving heat stress tolerance in Vigna crops.