The present disclosure provides a method of making a mammal (e.g., a rodent, such as a mouse) by integrating an intact polynucleotide sequence into a specific genomic locus of the mammal to result in a transgenic mammal. A transgenic mammal made by the methods of the present disclosure would contain a known copy number (e.g., one) of the inserted polynucleotide sequence at a predetermined location. The method involves introducing a site-specific recombinase and a targeting construct, containing a first recombination site and the polynucleotide sequence of interest, into the mammalian cell. The genome of the cell contains a second recombination site and recombination between the first and second recombination sites is facilitated by the site-specific, uni-directional recombinase. The result of the recombination is site-specific integration of the polynucleotide sequence of interest in the genome of the mammal. This inserted sequence is then also transmitted to the progeny of the mammal.