The K-type star TOI-2525 has an estimated mass of M = ${0.849}_{-0.033}^{+0.024}$ M ⊙ and radius of R = ${0.785}_{-0.007}^{+0.007}$ R ⊙ observed by the TESS mission in 22 sectors (within sectors 1 and 39). The TESS light curves yield significant transit events of two companions, which show strong transit timing variations (TTVs) with a semiamplitude of ~6 hr. We performed TTV dynamical and photodynamical light-curve analysis of the TESS data combined with radial velocity measurements from FEROS and PFS, and we confirmed the planetary nature of these companions. The TOI-2525 system consists of a transiting pair of planets comparable to Neptune and Jupiter with estimated dynamical masses of m b = ${0.088}_{-0.004}^{+0.005}$ and m c = ${0.709}_{-0.033}^{+0.034}$ M Jup, radii of r b = ${0.88}_{-0.02}^{+0.02}$ and r c = ${0.98}_{-0.02}^{+0.02}$ R Jup, and orbital periods of P b = ${23.288}_{-0.002}^{+0.001}$ and P c = ${49.260}_{-0.001}^{+0.001}$ days for the inner and outer planet, respectively. The period ratio is close to the 2:1 period commensurability, but the dynamical simulations of the system suggest that it is outside the mean-motion resonance (MMR) dynamical configuration. Object TOI-2525 b is among the lowest-density Neptune-mass planets known to date, with an estimated median density of ρ b = ${0.174}_{-0.015}^{+0.016}$ g cm-3. The TOI-2525 system is very similar to the other K dwarf systems discovered by TESS, TOI-2202 and TOI-216, which are composed of almost identical K dwarf primaries and two warm giant planets near the 2:1 MMR. ∗ Based on observations collected at the European Organization for Astronomical Research in the Southern Hemisphere under MPG program 0104.A-9007. This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile.