The origin of r-process elements remains unidentified and still puzzles us . The recent discovery of evidence for the ejection of r-process elements from a short-duration \gamma -ray burst singled out neutron star mergers ( NSMs ) as their origin . In contrast , core-collapse supernovae are ruled out as the main origin of heavy r-process elements ( A > 110 ) by recent numerical simulations . However , the properties characterizing NSM events - their rarity and high yield of r-process elements per event - have been claimed to be incompatible with the observed stellar records on r-process elements in the Galaxy . We add to this picture with our results , which show that the observed constant [ r-process/H ] ratio in faint dwarf galaxies and one star unusually rich in r-process in the Sculptor galaxy agree well with this rarity of NSM events . Furthermore , we found that a large scatter in the abundance ratios of r-process elements to iron in the Galactic halo can be reproduced by a scheme that incorporates an assembly of various protogalactic fragments , in each of which r-process elements supplied by NSMs pervade the whole fragment while supernovae distribute heavy elements only inside the regions swept up by the blast waves . Our results demonstrate that NSMs occurring at Galactic rate of 12-23 Myr ^ { -1 } are the main site of r-process elements , and we predict the detection of gravitational waves from NSMs at a high rate with upcoming advanced detectors .