Integrase is an essential retroviral enzyme that binds both termini of linear viral DNA and inserts them into a host cell chromosome. The structure of full-length retroviral integrase, either separately or in complex with DNA, has been lacking. Furthermore, although clinically useful inhibitors of HIV integrase have been developed, their mechanism of action remains speculative. Here we present a crystal structure of full-length integrase from the prototype foamy virus in complex with its cognate DNA. The structure shows the organization of the retroviral intasome comprising an integrase tetramer tightly associated with a pair of viral DNA ends. All three canonical integrase structural domains are involved in extensive protein-DNA and protein-protein interactions. The binding of strand-transfer inhibitors displaces the reactive viral DNA end from the active site, disarming the viral nucleoprotein complex. Our findings define the structural basis of retroviral DNA integration, and will allow modelling of the HIV-1 intasome to aid in the development of antiretroviral drugs.