The Dark Energy Spectroscopic Instrument (DESI) survey will measure large-scale structures using quasars as direct tracers of dark matter in the redshift range 0.9 2.1. We present several methods to select candidate quasars for DESI, using input photometric imaging in three optical bands (g, r, z) from the DESI Legacy Imaging Surveys and two infrared bands (W1, W2) from the Wide-field Infrared Survey Explorer. These methods were extensively tested during the Survey Validation of DESI. In this paper, we report on the results obtained with the different methods and present the selection we optimized for the DESI main survey. The final quasar target selection is based on a random forest algorithm and selects quasars in the magnitude range of 16.5 2.1), exceeding the project requirements by 20%. The redshift distribution of the selected quasars is in excellent agreement with quasar luminosity function predictions
