This paper reports on the study of the following: (a) the influence of the composition of poly(ethylene oxide)-poly(butylene terephthalate) (PEO-PBT) block copolymers on the solubility of water vapor; (b) the thermodynamic quantities governing the solubility of water vapor in these polymers. The block copolymers examined differ with respect to their hydrophilic block length (PEO segment) and the weight ratio between the hard hydrophobic PBT segment and the soft hydrophilic PEO segment. Water sorption isotherms, determined gravimetrically, are of Flory-Huggins type, exhibiting a linear relation between weight uptake and vapor activity at low activities and a sharp increase (convex shape) at higher activities. The Flory-Huggins interaction parameter decreases as the concentration of water inside the polymer increases. Its numerical value strongly depends on the polymeric structure: an increase of the soft hydrophilic PEO block length and PEO content both lead to a decrease of the interaction parameter. Solvation Gibbs energies, entropies, and enthalpies, extracted from temperature-dependent sorption data, reveal that (1) water-polymer interactions are stronger than water-water interactions in liquid water, (2) the water-polymer interactions become weaker at higher water vapor activities, and (3) the water sorption entropy increases with increasing vapor activity. The last observation (3) is responsible for the convex nature of the water sorption isotherm. Moreover, this effect depends on the structure of the polymer: the larger the PEO segment length and more PEO weight fraction the higher the solvation entropy and, consequently, the solubility of water vapor in the PEO-PBT block copolymer.