We have detected the H2O center dot DMA and H2O center dot TMA (DMA, dimethylamine; TMA, trimethylamine) bimolecular complexes at room temperature in the gas phase using Fourier transform infrared spectroscopy. For both complexes, five vibrational bands associated with the H2O molecule are observed and assigned. Within a reduced dimensional local mode framework, we set up a six-dimensional model, including the three H2O vibrational modes and three of the six intermolecular modes, all described with internal curvilinear coordinates. The single points on the potential energy surface and Eckart corrected dipole moment surface are calculated with the CCSD(T)-F12a/cc-pVDZ-F12 method. Combining the measured and calculated transition intensities, we determine the Gibbs energy of complex formation of both complexes from each of the observed bands. The multiple determinations give similar Gibbs energies, for each complex, and increase the confidence in the combined experimental and theoretical approach, and improve the accuracy of the determined Gibbs energies. The average Gibbs energies of complex formation are found to be 5.0 +/- 0.2 and 3.8 +/- 0.2 kJ/mol for H2O center dot DMA and H2O center dot TMA, respectively. In addition to the experimental uncertainty, there is a potential error on the calculated intensities corresponding to 0.4 kJ/mol. However, the small spread among the four determinations suggests that this error is even less. The Gibbs energies of these complexes serve as accurate benchmarks for theoretical approaches that are prevalent in hydrogen bonding and nucleation studies.