Hydroperoxides are formed in significant amounts in the atmosphere by oxidation of volatile organic compounds and are key in aerosol formation. In a room-temperature experiment, we detected the formation of bimolecular complexes of tert-butyl hydroperoxide (t-BuOOH) and the corresponding alcohol tert-butanol (t-BuOH), with dimethyl ether (DME) as the hydrogen-bond acceptor. Using a combination of Fourier-transform infrared spectroscopy and quantum chemical calculations, we compare the strength of the OH-O hydrogen bond and the total strength of complexation. We find that, both in terms of observed red shifts and determined equilibrium constants, t-BuOOH is a significantly better hydrogen-bond donor than t-BuOH, a result that is backed by a number of calculated parameters and can be explained by a weaker OH bond in the hydroperoxide. On the basis of combined experimental and theoretical results, we find that the hydroperoxide complex is stabilized by ∼4 kJ/mol (Gibbs free energy) more than the alcohol complex. Measured red shifts show the same trend in hydrogen-bond strength with trimethylamine (N acceptor atom) and dimethyl sulfide (S acceptor atom) as the hydrogen-bond acceptors.