Context. Transiting planets around young stars are key benchmarks for our understanding of planetary systems. One such candidate, TOI-179, was identified around the K dwarf HD 18599 by TESS.Aims. We present the confirmation of the transiting planet and the characterization of the host star and of the TOI-179 system over a broad range of angular separations.Methods. We exploited the TESS photometric time series, intensive radial velocity monitoring performed with HARPS, and deep high-contrast imaging observations obtained with SPHERE and NACO at VLT. The inclusion of Gaussian process regression analysis was effective to properly model the magnetic activity of the star and identify the Keplerian signature of the transiting planet.Results. The star, with an age of 400 & PLUSMN;100 Myr, is orbited by a transiting planet with period 4.137436 days, mass 24 & PLUSMN;7 M-& OPLUS;, radius 2.62(-0.12)(+0.15) R-& OPLUS;, and significant eccentricity (0.34(-0.09)(+0.07)). Adaptive optics observations identified a low-mass companion at the boundary between brown dwarfs and very low-mass stars (mass derived from luminosity 83(-6)(+4) M-J) at a very small projected separation (84.5 mas, 3.3 au at the distance of the star). Coupling the imaging detection with the long-term radial velocity trend and the astrometric signature, we constrained the orbit of the low-mass companion, identifying two families of possible orbital solutions.Conclusions. The TOI-179 system represents a high-merit laboratory for our understanding of the physical evolution of planets and other low-mass objects and of how the planet properties are influenced by dynamical effects and interactions with the parent star.