Aims. Our aim is to characterize the conditions in the nearest interstellar cloud. Methods. We analyze interstellar absorption features in the full UV spectrum of the nearby (d = 24 pc) B8 IVn star α Leo (Regulus). Observations were obtained with STIS at high resolution and high signal-to-noise ratio by the HST ASTRAL Treasury program. We derive column densities for many key atomic species and interpret their partial ionizations. Results. The gas in front of α Leo exhibits two absorption components. The main one is kinematically identified as the local interstellar cloud (LIC) that surrounds the Sun. The second component is shifted by +5.6 km s-1 relative to the main component, in agreement with results for other lines of sight in this region of the sky, and shares its ionization and physical conditions. The excitation of the C II fine-structure levels and the ratio of Mg I to Mg II reveal a temperature T = 6500 (+750, −600) K and electron density n(e) = 0.11 (+0.025, −0.03) cm-3. Our investigation of the ionization balance yields the ion fractions for 10 different atoms and indicates that about 1/3 of the hydrogen atoms are ionized. Metals are significantly depleted onto grains, with sulfur showing [S/H] ~ −0.27. N(H I) = 1.9 (+0.9, −0.6) × 1018 cm-3, which indicates that this partly neutral gas occupies only 2 to 8 parsecs (about 13%) of the space toward the star, with the remaining volume being filled with a hot gas that emits soft X-rays. We do not detect any absorption features from the highly ionized species that could be produced in an interface between the warm medium and the surrounding hot gas, possibly because of non-equilibrium conditions or a particular magnetic field orientation that reduces thermal conduction. Finally, the radial velocity of the LIC agrees with that of the Local Leo Cold Cloud, indicating that they may be physically related.