A new survey is presented, which explores the second data release of the ESA-Gaia mission, in order to search for stellar companions of exoplanet host stars, located at distances closer than about 500pc around the Sun. In total, 176 binaries, 27 hierarchical triples, and one hierarchical quadruple system are detected among more than 1300 exoplanet host stars, whose multiplicity is investigated, yielding a multiplicity rate of the exoplanet host stars of at least about 15 per cent. The detected companions and the exoplanet host stars are equidistant and share a common proper motion, as it is expected for gravitationally bound stellar systems, proven with their accurate Gaia astrometry. The companions exhibit masses in the range between about 0.078 and 1.4M_{sun}_ with a peak in their mass distribution between 0.15 and 0.3M{sun}_. The companions are separated from the exoplanet host stars by about 20 up to 9100au, but are found most frequently within a projected separation of 1000au. While most of the detected companions are early M dwarfs, eight white dwarf companions of exoplanet host stars are also identified in this survey, whose true nature is revealed with their photometric properties. Hence, these degenerated companions and the exoplanet host stars form evolved stellar systems with exoplanets, which have survived (physically but also dynamically) the post-main-sequence evolution of their former primary star.