Aims. We aim to detect planetary companions to young stars with debris disks via the radial velocity method. Methods. We observed HD 114082 during April 2018–August 2022 as one of the targets of our RVSPY program (Radial Velocity Survey for Planets around Young stars). We use the FEROS spectrograph, mounted to the MPG/ESO 2.2 m telescope in Chile, to obtain high signal-to-noise spectra and time series of precise radial velocities (RVs). Additionally, we analyze archival HARPS spectra and TESS photometric data. We use the CERES, CERES++ and SERVAL pipelines to derive RVs and activity indicators and ExoStriker for the independent and combined analysis of the RVs and TESS photometry. Results. We report the discovery of a warm super-Jovian companion around HD 114082 based on a 109.8±0.4 day signal in the combined RV data from FEROS and HARPS, and on one transit event in the TESS photometry. The best-fit model indicates a 8.0±1.0 M Jup companion with a radius of 1.00±0.03  R Jup in an orbit with a semi-major axis of 0.51±0.01 au and an eccentricity of 0.4±0.04. The companions orbit is in agreement with the known near edge-on debris disk located at ∼28 au. HD 114082 b is possibly the youngest (15±6 Myr), and one of only three young (< 100 Myr) giant planetary companions for which both their mass and radius have been determined observationally. It is probably the first properly model-constraining giant planet that allows distinguishing between hot and cold-start models. It is significantly more compatible with the cold-start model.