Nuclear star clusters (NSCs) are the densest stellar systems in the Universe. These clusters can be found at the centre of all galaxy types but tend to favour galaxies of intermediate stellar mass around 109M circle dot (refs. 1,2). At present, two main processes are under debate to explain their formation: in situ star formation from gas infall3 and migration and merging of globular clusters (GCs) caused by dynamical friction4. Studies5, 6, 7, 8-9 of NSC stellar populations suggest that the former predominates in massive galaxies, whereas the latter prevails in dwarf galaxies, and both contribute equally at intermediate mass. However, until now, no ongoing merger of GCs has been observed to confirm this scenario. Here we report the serendipitous discovery of five dwarf galaxies with complex nuclear regions, characterized by multiple nuclei and tidal tails, using high-resolution images from the Hubble Space Telescope. These structures have been reproduced in complementary N-body simulations, supporting the interpretation that they result from migrating and merging of star clusters. The small detection rate and short simulated timescales (below 100 Myr) of this process may explain why this has not been observed previously. This study highlights the need for large surveys with high resolution to fully map the migration scenario steps.