We report the spectroscopic confirmation of the Kepler object of interest KOI-183.01 (Kepler-423b), a half-Jupiter mass planet transiting an old solar-like star every 2.7 days. Our analysis is the first to combine the full Kepler photometry (quarters 1-17) with high-precision radial velocity measurements taken with the FIES spectrograph at the Nordic Optical Telescope. We simultaneously modelled the photometric and spectroscopic data-sets using Bayesian approach coupled with Markov chain Monte Carlo sampling. We found that the Kepler pre-search data conditioned light curve of Kepler-423 exhibits quarter-to-quarter systematic variations of the transit depth, with a peak-to-peak amplitude of ~4.3% and seasonal trends reoccurring every four quarters. We attributed these systematics to an incorrect assessment of the quarterly variation of the crowding metric. The host star Kepler-423 is a G4 dwarf with M⋆ = 0.85 ± 0.04 M⊙, R⋆ = 0.95 ± 0.04 R⊙, Teff= 5560 ± 80 K, [M/H] = - 0.10 ± 0.05 dex, and with an age of 11 ± 2 Gyr. The planet Kepler-423b has a mass of Mp= 0.595 ± 0.081MJup and a radius of Rp= 1.192 ± 0.052RJup, yielding a planetary bulk density of ρp = 0.459 ± 0.083 g cm-3. The radius of Kepler-423b is consistent with both theoretical models for irradiated coreless giant planets and expectations based on empirical laws. The inclination of the stellar spin axis suggests that the system is aligned along the line of sight. We detected a tentative secondary eclipse of the planet at a 2σ confidence level (ΔFec = 14.2 ± 6.6 ppm) and found that the orbit might have asmall non-zero eccentricity of 0.019+0.028-0.014. With a Bond albedo of AB = 0.037 ± 0.019, Kepler-423b is one of the gas-giant planets with the lowest albedo known so far. Based on observations obtained with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias, in time allocated by OPTICON and the Spanish Time Allocation Committee (CAT).The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement number RG226604 (OPTICON) and 267251 (AstroFIt).