We confirm the planetary nature of Kepler-539 b (aka Kepler object of interest K00372.01), a giant transiting exoplanet orbiting a solar-analogue G2V star. The mass of Kepler-539 b was accurately derived thanks to a series of precise radial velocity measurements obtained with the CAFE spectrograph mounted on the CAHA 2.2-m telescope. A simultaneous fit of the radial-velocity data and Kepler photometry revealed that Kepler-539 b is a dense Jupiter-like planet with a mass of M-p = 0.97 +/- 0.29 M-Jup and a radius of R-p = 0.747 +/- 0.018 R-Jup, making a complete circular revolution around its parent star in 125.6 days. The semi-major axis of the orbit is roughly 0.5 au, implying that the planet is at approximate to 0.45 au from the habitable zone. By analysing the mid-transit times of the 12 transit events of Kepler-539 b recorded by the Kepler spacecraft, we found a clear modulated transit time variation (TTV), which is attributable to the presence of a planet c in a wider orbit. The few timings available do not allow us to precisely estimate the properties of Kepler-539 c and our analysis suggests that it has a mass between 1.2 and 3.6 M-Jup, revolving on a very eccentric orbit (0.4 < e <= 0.6) with a period larger than 1000 days. The high eccentricity of planet c is the probable cause of the TTV modulation of planet b. The analysis of the CAFE spectra revealed a relatively high photospheric lithium content, A(Li) = 2.48 +/- 0.12 dex, which, together with both a gyrochronological and isochronal analysis, suggests that the parent star is relatively young.