The statistical associating fluid theory for potentials of variable range plus dipole (SAFT-VR+D) is extended to study associating dipolar fluids. In the SAFT-VR+D approach dipolar interactions are taken into account through the use of the generalized mean spherical approximation to describe a reference fluid of dipolar square-well segments. This enables the effect of the dipolar interactions on the thermodynamics and structure of fluids to be explicitly described. Predictions for the thermodynamic properties and phase behavior of dipolar associating square-well monomers with one, two, and four association sites are considered and compared with new isothermal-isobaric and Gibbs ensemble Monte Carlo simulation data. The results show that the SAFT-VR+D equation provides a good description of the phase behavior of dipolar associating fluids. Additionally we have applied the new theoretical approach to study the vapor pressure and saturated liquid density of water.