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Context. The collection of high-quality photometric data by space telescopes, such as the completed Kepler mission and the ongoing TESS program, is revolutionizing the area of white-dwarf asteroseismology. Among the different kinds of pulsating white dwarfs, there are those that have He-rich atmospheres, and they are called DBVs or V777 Her variable stars. The archetype of these pulsating white dwarfs, GD 358, is the focus of the present paper. Aims. We report a thorough asteroseismological analysis of the DBV star GD 358 (TIC 219074038) based on new high-precision photometric data gathered by the TESS space mission combined with data taken from the Earth. Methods. We reduced TESS observations of the DBV star GD 358 and performed a detailed asteroseismological analysis using fully evolutionary DB white-dwarf models computed accounting for the complete prior evolution of their progenitors. We assessed the mass of this star by comparing the measured mean period separation with the theoretical averaged period spacings of the models, and we used the observed individual periods to look for a seismological stellar model. We detected potential frequency multiplets for GD 358, which we used to identify the harmonic degree (l) of the pulsation modes and rotation period. Results. In total, we detected 26 periodicities from the TESS light curve of this DBV star using standard pre-whitening. The oscillation frequencies are associated with nonradial g(gravity)-mode pulsations with periods from ∼422 s to ∼1087 s. Moreover, we detected eight combination frequencies between ∼543 s and ∼295 s. We combined these data with a huge amount of observations from the ground. We found a constant period spacing of 39.25 ± 0.17 s, which helped us to infer its mass (M* = 0.588 ± 0.024 M_☉) and constrain the harmonic degree l of the modes. We carried out a period-fit analysis on GD 358, and we were successful in finding an asteroseismological model with a stellar mass (M* = 0.584_–0.019^+0.025M_☉, compatible with the stellar mass derived from the period spacing, and in line with the spectroscopic mass (M* = 0.560 ± 0.028 M_☉). In agreement with previous works, we found that the frequency splittings vary according to the radial order of the modes, suggesting differential rotation. Obtaining a seismological model made it possible to estimate the seismological distance (d_seis = 42.85 ± 0.73 pc) of GD 358, which is in very good accordance with the precise astrometric distance measured by Gaia EDR3 (π = 23.244 ± 0.024, d_Gaia = 43.02 ± 0.04 pc). Conclusions. The high-quality data measured with the TESS space telescope, used in combination with data taken from ground-based observatories, provides invaluable information for conducting asteroseismological studies of DBV stars, analogously to what happens with other types of pulsating white-dwarf stars. The currently operating TESS mission, together with the advent of other similar space missions and new stellar surveys, will give an unprecedented boost to white dwarf asteroseismology.