Drought is one of the complex abiotic stresses that affect the growth and production of wheat in arid and semiarid countries. In this study, a set of 172 diverse spring wheat genotypes from 20 different countries were assessed under drought stress at the seedling stage. Besides seedling length, two types of traits were recorded, namely: tolerance traits (days to wilting, leaf wilting, and the sum of leaf wilting), and recovery traits (days to regrowth, regrowth biomass, and drought survival rate). In addition, tolerance index, recovery index, and drought tolerance index (DTI) were estimated to select the most drought tolerant genotypes. Moreover, leaf protein content (P), amino acid (AM), proline content (PRO), glucose (G), fructose (F), and total soluble carbohydrates (TSC) were measured under control and drought conditions to study the changes in each physiological trait due to drought stress. All genotypes showed a high significant genetic variation in all the physio-morphological traits scored under drought stress. High phenotypic and genotypic correlations were found among all seedling morphological traits. Among the studied indices, the drought tolerance index (DTI) had the highest phenotypic and genotypic correlations with all tolerance and recovery traits. The broad-sense heritability (H2) estimates were high for morphological traits (83.85–92.27), while the physiological traits ranged from 96.41 to 98.68 under the control conditions and from 97.13 to 99.99 under drought stress. The averages of the physiological traits (proteins, amino acids, proline, glucose, fructose, and total soluble carbohydrates) denoted under drought stress were higher than those recorded under well-watered conditions except for proteins. In this regard, amino acids, glucose, and total soluble carbohydrates had a significant correlation with all morphological traits. The selection for drought tolerance revealed 10 tolerant genotypes from different countries (8 genotypes from Egypt, one from Morocco, and one from the United States). These selected genotypes were screened for the presence of nine specific TaDREB1 alleles. Six primers were polymorphic among the selected genotypes. Genetic diversity among the selected genotypes was investigated using 21,450 SNP markers. The results of the study shed light on the different mechanisms for drought tolerance that wheat plants use to tolerate and survive under drought stress. The genetic analysis performed in this study suggested the most suitable genotypes for selective breeding at the seedling stage under water deficit.