Retroviral integrase can efficiently utilise nucleosomes for insertion of the reverse-transcribed viral DNA. In face of the structural constraints imposed by the nucleosomal structure, integrase gains access to the scissile phosphodiester bonds by lifting DNA off the histone octamer at the site of integration. To clarify the mechanism of DNA looping by integrase, we determined a 3.9 Å resolution structure of the prototype foamy virus intasome engaged with a nucleosome core particle. The structural data along with complementary single-molecule Förster resonance energy transfer measurements reveal twisting and sliding of the nucleosomal DNA arm proximal to the integration site. Sliding the nucleosomal DNA by approximately two base pairs along the histone octamer accommodates the necessary DNA lifting from the histone H2A-H2B subunits to allow engagement with the intasome. Thus, retroviral integration into nucleosomes involves the looping-and-sliding mechanism for nucleosomal DNA repositioning, bearing unexpected similarities to chromatin remodelers.