Context. Hypervelocity stars (HVSs) travel so fast that they may leave the Galaxy. The tidal disruption of a binary system by the supermassive black hole in the Galactic center is widely assumed to be their ejection mechanism. Aims. To test the hypothesis of an origin in the Galactic center using kinematic investigations, the current space velocities of the HVSs need to be determined. With the advent of Gaia’s second data release, accurate radial velocities from spectroscopy are complemented by proper motion measurements of unprecedented quality. Based on a new spectroscopic analysis method, we provide revised distances and stellar ages, both of which are crucial to unravel the nature of the HVSs. Methods. We reanalyzed low-resolution optical spectra of 14 HVSs from the MMT HVS survey using a new grid of synthetic spectra, which account for deviations from local thermodynamic equilibrium, to derive effective temperatures, surface gravities, radial velocities, and projected rotational velocities. Stellar masses, radii, and ages were then determined by comparison with stellar evolutionary models that account for rotation. Finally, these results were combined with photometric measurements to obtain spectroscopic distances. Results. The resulting atmospheric parameters are consistent with those of main sequence stars with masses in the range 2.5–5.0 M_⊙. The majority of the stars rotate at fast speeds, providing further evidence for their main sequence nature. Stellar ages range from 90 to 400 Myr and distances (with typical 1σ-uncertainties of about 10–15%) from 30 to 100 kpc. Except for one object (B 711), which we reclassify as A-type star, all stars are of spectral type B. Conclusions. The spectroscopic distances and stellar ages derived here are key ingredients for upcoming kinematic studies of HVSs based on Gaia proper motions.