We present a rigorous calculation of the contribution of water dimers to the absorption coefficient α(ν,T) in the millimeter and far infrared domains, over a wide range (276–310 K) of temperatures. This calculation relies on the explicit consideration of all possible transitions within the entire rovibrational bound state manifold of the dimer. The water dimer is described by the flexible 12-dimensional potential energy surface previously fitted to far IR transitions [ C. Leforestier et al., J. Chem. Phys. 117, 8710 (2002) ], and which was recently further validated by the good agreement obtained for the calculated equilibrium constant K_p(T) with experimental data [ Y. Scribano et al., J. Phys. Chem. A. 110, 5411 (2006) ]. Transition dipole matrix elements were computed between all rovibrational states up to an excitation energy of 750 cm⁻¹, and J = K = 5 rotational quantum numbers. It was shown by explicit calculations that these matrix elements could be extrapolated to much higher J values (J = 30). Transitions to vibrational states located higher in energy were obtained from interpolation of computed matrix elements between a set of initial states spanning the 0–750 cm⁻¹ range and all vibrational states up to the dissociation limit ( ∼ 1200 cm⁻¹). We compare our calculations with available experimental measurements of the water continuum absorption in the considered range. It appears that water dimers account for an important fraction of the observed continuum absorption in the millimeter region (0–10 cm⁻¹). As frequency increases, their relative contribution decreases, becoming small ( ∼ 3%) at the highest frequency considered ν = 944 cm⁻¹.