Leucaena leucocephala (Leucaena) is a leguminous tree widely cultivated in tropical and subtropical regions due to its strong environmental suitability for abiotic stresses, especially drought. However, the molecular mechanisms and key pathways involved in Leucaena's drought response require further elucidation. Here, we comparatively analyzed the physiological and early transcriptional responses of Leucaena leaves and roots under drought stress simulated by polyethylene glycol (PEG) treatments. Drought stress induced physiological changes in Leucaena seedlings, including decreases in relative water content (RWC) and increases in relative electrolyte leakage (REL), malondialdehyde (MDA), proline contents as well as antioxidant enzyme activities. In response to drought stress, 6461 and 8295 differentially expressed genes (DEGs) were identified in the leaves and roots, respectively. In both tissues, the signaling transduction pathway of plant hormones was notably the most enriched. Specifically, abscisic acid (ABA) biosynthesis and signaling related genes (NCED, PP2C, SnRK2 and ABF) were strongly upregulated particularly in leaves. The circadian rhythm, DNA replication, alpha-linolenic acid metabolism, and secondary metabolites biosynthesis related pathways were repressed in leaves, while the glycolysis/gluconeogenesis and alpha-linolenic acid metabolism and amino acid biosynthesis processes were promoted in roots. Furthermore, heterologous overexpression of Leucaena drought-inducible genes (PYL5, PP2CA, bHLH130, HSP70 and AUX22D) individually in yeast increased the tolerance to drought and heat stresses. Overall, these results deepen our understanding of the tissue-specific mechanisms of Leucaena in response to drought and provide target genes for future drought-tolerance breeding engineering in crops.