Context. The origin of the observed diversity of planetary system architectures is one of the main topics of exoplanetary research. The detection of a statistically significant sample of planets around young stars allows us to study the early stages of planet formation and evolution, but only a handful are known so far. In this regard a considerable contribution is expected from the NASA TESS satellite, which is now performing a survey of ~85% of the sky to search for short-period transiting planets. Aims. In its first month of operation TESS found a planet candidate with an orbital period of 8.14 days around a member of the Tuc-Hor young association (~40 Myr), the G6V main component of the binary system DS Tuc. If confirmed, it would be the first transiting planet around a young star suitable for radial velocity and/or atmospheric characterisation. Our aim is to validate the planetary nature of this companion and to measure its orbital and physical parameters. Methods. We obtained accurate planet parameters by coupling an independent reprocessing of the TESS light curve with improved stellar parameters and the dilution caused by the binary companion; we analysed high-precision archival radial velocities to impose an upper limit of about 0.1 M_Jup on the planet mass; we finally ruled out the presence of external companions beyond 40 au with adaptive optics images. Results. We confirm the presence of a young giant (R = 0.50 R_Jup) planet having a non-negligible possibility to be inflated (theoretical mass ≲ 20 M_⊕) around DS Tuc A. We discuss the feasibility of mass determination, Rossiter-McLaughlin analysis, and atmosphere characterisation allowed by the brightness of the star.