We report the discovery of 74 new pulsating DA white dwarf stars, or ZZ Cetis, from the data obtained by the Transiting Exoplanet Survey Satellite mission, from Sectors 1 to 39, corresponding to the first 3 cycles. This includes objects from the Southern hemisphere (Sectors 1-13 and 27-39) and the Northern hemisphere (Sectors 14-26), observed with 120 s- and 20 s-cadence. Our sample likely includes 13 low-mass and one extremely low-mass white dwarf candidate, considering the mass determinations from fitting Gaia magnitudes and parallax. In addition, we present follow-up time series photometry from ground-based telescopes for 11 objects, which allowed us to detect a larger number of periods. For each object, we analysed the period spectra and performed an asteroseismological analysis, and we estimate the structure parameters of the sample, i.e. stellar mass, effective temperature, and hydrogen envelope mass. We estimate a mean asteroseismological mass of < M-sis & rang; = 0.635 +/- 0.015 M-circle dot, excluding the candidate low or extremely low-mass objects. This value is in agreement with the mean mass using estimates from Gaia data, which is < M-phot & rang; = 0.631 +/- 0.040 M-circle dot, and with the mean mass of previously known ZZ Cetis of < M-*& rang; = 0.644 +/- 0.034 M-circle dot. Our sample of 74 new bright ZZ Cetis increases the number of known ZZ Cetis by similar to 20 per cent.