We develop an automated technique for detecting damped Ly{alpha} absorbers (DLAs) along spectroscopic lines of sight to quasi-stellar objects (QSOs or quasars). The detection of DLAs in large-scale spectroscopic surveys such as SDSS III sheds light on galaxy formation at high redshift, showing the nucleation of galaxies from diffuse gas. We use nearly 50000 QSO spectra to learn a novel tailored Gaussian process model for quasar emission spectra, which we apply to the DLA detection problem via Bayesian model selection. We propose models for identifying an arbitrary number of DLAs along a given line of sight. We demonstrate our method's effectiveness using a large-scale validation experiment, with excellent performance. We also provide a catalogue of our results applied to 162858 spectra from SDSS-III data release 12.