Modern hexaploid wheat has several diploid and tetraploid predecessors. Morpho-physiological adaptation and the adaptation to drought of these different ploidy wheat species is largely unknown. To investigate the adaptation to drought stress, eight accesssions (two wild diploid (2n) accessions of Aegilops tauschii Coss., two domesticated diploid (2n) accessions of Triticum monococcum L., two domesticated tetraploid (4n) accessions of Triticum dicoccum Schrank ex Schübl. and two domesticated hexaploid (6n) accessions of Triticum aestivum L.) were exposed to three water regimes: (i) well-watered control (WW, 80% field capacity (FC)), (ii) moderate water stress (MS, 50% FC), and (iii) severe water stress (SS, 25% FC) from 30 days after sowing to maturity. The results showed that accession (A), water regime (W), and the interaction of A × W significantly affected yield, morpho-physiological traits, biochemical characteristics and biomass allocation. In the WW treatment, the aboveground biomass, ear biomass, grain yield and harvest index increased, whereas the number of spikes and spikelets per plant decreased from accessions of T. monococcum to T. dicoccum to T. aestivum. Across all accessions, yields decreased by 29% under moderate water stress and 61% under severe water stress. In all three water regimes, yields were positively correlated with photosynthesis (Pn) per plant (Pn × leaf area) at jointing and anthesis, largely the result of the differences and changes in leaf area. Water use efficiency for grain (WUEG) decreased by 2–6% in T. monococcum, but it increased by 15–16% in T. dicoccum and T. aestivum under drought stress. Analysis of the allometric relationships between aboveground biomass (MAB) and root biomass (Mroot) in the different species indicated that less biomass was allocated to roots with greater polyploidy while more biomass was allocated to roots with drought in A. tauschii, but not in the domesticated species. We conclude that domestication, selection and breeding of higher ploidy wheat has increased wheat yields primarily by increasing aboveground biomass and harvest index, increases that were maintained under water stress.