Context. The detection of the He I λ10 830 Å triplet in exoplanet atmospheres has opened a new window for probing planetary properties, including atmospheric escape. Unlike Lyman α, the triplet is significantly less affected by interstellar medium (ISM) absorption. Sufficient X-ray and extreme ultraviolet (XUV) stellar irradiation may trigger the formation of the He I triplet via photoionization and posterior recombination processes in the planet atmospheres. Only a weak trend between stellar XUV emission and the planetary He I strength has been observed so far. Aims. We aim to confirm this mechanism for producing near-infrared He I absorption in exoplanetary atmospheres by examining a substantial sample of planetary systems. Methods. We obtained homogeneous measurements of the planetary He I line equivalent width and consistently computed the stellar XUV ionizing irradiation. Our first step was to derive new coronal models for the planet-host stars. We used updated data from the X-exoplanets database, archival X-ray spectra of M-type stars (including AU Mic and Proxima Centauri), and new XMM-Newton X-ray data recently obtained for the CARMENES project. These data were complemented at longer wavelengths with publicly available HST, FUSE, and EUVE spectra. A total of 75 stars are carefully analyzed to obtain a new calibration between X-ray and extreme ultraviolet (EUV) emission. Results. Two distinct relationships between stellar X-ray emission (5–100 Å) and EUVH (100–920 Å) or EUVHe (100–504 Å) radiation are obtained to scale the emission from late-type (F to M) stellar coronae. A total of 48 systems with reported planetary He I λ 10 830 Å studies, including 21 positive detections and 27 upper limits, exhibit a robust relationship between the strength of the planetary He I feature and the ionizing XUVHe received by the planet, corrected by stellar and planetary radii, as well as the planet's gravitational potential. Some outliers could be explained by a different atmospheric composition or the lack of planetary gaseous atmospheres. This relation may serve as a guide to predict the detectability of the He I λ 10 830 Å absorption in exoplanet atmospheres.