Catalysis of the covalent insertion of double-stranded retroviral DNA into host DNA. Proceeds by an endonucleolytic cleavage at each 3'-OH extremity of the viral genome, named 3'-processing, followed by a strand transfer reaction leading to the insertion of the processed viral DNA into the target DNA by a trans-esterification mechanism. [ http://www.ncbi.nlm.nih.gov/pubmed/19091057 ]