Context. The current architecture of a given multi-planetary system is a key fingerprint of its past formation and dynamical evolution history. Long-term follow-up observations are key to complete their picture. Aims. In this paper, we focus on the confirmation and characterization of the components of the TOI-969 planetary system, where TESS detected a Neptune-size planet candidate in a very close-in orbit around a late K-dwarf star. Methods. We use a set of precise radial velocity observations from HARPS, PFS, and CORALIE instruments covering more than two years in combination with the TESS photometric light curve and other ground-based follow-up observations to confirm and characterize the components of this planetary system. Results. We find that TOI-969 b is a transiting close-in (P_b ~ 1.82 days) mini-Neptune planet (m_b = 9.1_−1.0^+1.1 M_⊕, R_b = 2.765_−0.097^+0.088 R_⊕), placing it on the lower boundary of the hot-Neptune desert (T_eq,b = 941 ± 31 K). The analysis of its internal structure shows that TOI-969 b is a volatile-rich planet, suggesting it underwent an inward migration. The radial velocity model also favors the presence of a second massive body in the system, TOI-969 c, with a long period of P_c = 1700₋₂₈₀⁺²⁹⁰ days, a minimum mass of m_c sin i_c = 11.3_−0.9^+1.1 M_Jup, and a highly eccentric orbit of e_c = 0.628_−0.036^+0.043. Conclusions. The TOI-969 planetary system is one of the few around K-dwarfs known to have this extended configuration going from a very close-in planet to a wide-separation gaseous giant. TOI-969 b has a transmission spectroscopy metric of 93 and orbits a moderately bright (G = 11.3 mag) star, making it an excellent target for atmospheric studies. The architecture of this planetary system can also provide valuable information about migration and formation of planetary systems.