We performed an intensive radial velocity monitoring of XO-2S, the wide companion of the transiting planet-host XO-2N, using HARPS-N at TNG in the framework of the GAPS programme. The radial velocity measurements indicate the presence of a new planetary system formed by a planet that is slightly more massive than Jupiter at 0.48 au and a Saturn-mass planet at 0.13 au. Both planetary orbits are moderately eccentric and were found to be dynamically stable. There are also indications of a long-term trend in the radial velocities. This is the first confirmed case of a wide binary whose components both host planets, one of which is transiting, which makes the XO-2 system a unique laboratory for understanding the diversity of planetary systems. Based on observations made with the Italian Telescopio Nazionale Galileo (TNG) operated on the island of La Palma by the Fundacion Galileo Galilei of the INAF at the Spanish Observatorio del Roque de los Muchachos of the IAC as part of the programme Global Architecture of Planetary Systems (GAPS), and on observations made at Asiago, Serra La Nave, and Valle D'Aosta observatories.Table 2 and Fig. 3 are available in electronic form at http://www.aanda.org