We present a catalogue of white dwarf candidates selected from Gaia early data release three (EDR3). We applied several selection criteria in absolute magnitude, colour, and Gaia quality flags to remove objects with unreliable measurements while preserving most stars compatible with the white dwarf locus in the Hertzsprung-Russell diagram. We then used a sample of over 30 000 spectroscopically confirmed white dwarfs and contaminants from the Sloan Digital Sky Survey (SDSS) to map the distribution of these objects in the Gaia absolute magnitude-colour space. Finally, we adopt the same method presented in our previous Gaia DR2 work to calculate a probability of being a white dwarf (Pwd) for $\simeq$1.3 million sources which passed our quality selection. The Pwd values can be used to select a sample of $\simeq$359 000 high-confidence white dwarf candidates in the magnitude range 8< G <21. We calculated stellar parameters (effective temperature, surface gravity, and mass) for all these stars by fitting Gaia astrometry and photometry with synthetic models. We estimate an upper limit of 93 per cent for the overall completeness of our catalogue for white dwarfs with G $\leq$20 mag and effective temperature (Teff)>7000K, at high Galactic latitudes (|b|>20{\deg}). Alongside the main catalogue we include a reduced-proper-motion extension containing $\simeq$10 200 white dwarf candidates with unreliable parallax measurements which could, however be identified on the basis of their proper motion. We also performed a cross-match of our catalogues with SDSS DR16 spectroscopy and provide spectral classification based on visual inspection for all resulting matches.