The volume, energy, entropy, and Helmholtz free energy of mixing of the seven simplest primary alkanolamine molecules, i.e., monoethanolamine, monoisopropanolamine, 2-amino-propan-l-ol, 2-amino butan-l-ol, 2-amino-2-methyl-propan-1-ol, 1-amino-2-methyl-propan-2-ol, and 1-amino-butan-2-ol, with water is investigated by extensive computer simulations and thermodynamic integration. To check the force field dependence of the results, all calculations are repeated with two commonly used water models, namely, SPC/E and TIP4P. The obtained results show that the thermodynamics of mixing of alkanolamines and water is largely independent from the type of the alkanolamine molecule. The Helmholtz free energy of mixing is found to be negative for all alkanolamines at every composition, in accordance with the experimentally known full miscibility of these molecules and water. This free energy decrease occurring upon mixing is found to be clearly of energetic origin, as the energy of mixing always turns out to be negative in the entire composition range, while the entropy of mixing is also negative up to high alkanolamine mole fractions. The obtained results suggest that alkanolamines form, on average, stronger hydrogen bonds with water than what is formed by two water molecules, and they induce some ordering of the hydrating water molecules both through the hydrophobic hydration of their side chains and through the strong hydrogen bonding.