Context: Planets around evolved stars exhibit different properties than those orbiting main-sequence stars. One of the most notable differences is the paucity of planets orbiting at short distance from giant stars (a < 0.5 AU). Detecting these rare close-in planets can shed light on planetary system formation and evolution mechanisms. Aims: We study the Kepler object KOI-1299, an evolved star ascending the red giant branch. We aim at confirming the planetary nature of the Jupiter-like transit signal recurring every ~52.5 days, and characterizing the orbital elements of the system. Methods: We derive radial velocities from multi-epoch high-resolution spectra of KOI-1299 acquired with CAFE at the 2.2m telescope of Calar Alto Observatory and FIES at the 2.56m Nordic Optical Telescope of Roque de los Muchachos Observatory. Results: We confirm the planetary nature of the transiting object KOI-1299b. We find a planetary mass of Mp=5.86 +\- 0.05 Mjup and an eccentricity of e=0.479 +\- 0.004. With a semi-major axis of a=0.304 +\- 0.007 AU, KOI-1299b is the first bona-fide warm-Jupiter detected to transit a giant star. We also find a radial velocity linear trend of 0.44 +\- 0.04 m / (sec day) , which suggests the presence of a third object in the system. Current models of planetary evolution in the post main-sequence phase predict that KOI-1299b will be most likely engulfed by its host star before the latter reaches the tip of the red giant branch.