Genome engineering benefits from the availability of DNA modifying enzymes that have different target specificities and have optimized performance in different cell types. This variety of site-specific enzymes can be used to develop complex genome engineering applications at multiple loci. Although eight yeast site-specific tyrosine recombinases are known, only Flp is actively used in genome engineering. To expand the pool of the yeast site-specific tyrosine recombinases capable of mediating genome manipulations in mammalian cells, we engineered and analyzed variants of two tyrosine recombinases: R and TD. The activity of the evolved variants, unlike the activity of the native R and TD recombinases, is suitable for genome engineering in E. coli and mammalian cells. Unexpectedly, we found that R recombinase benefits from the shortening of its C-terminus. We also found that the activity of wild-type R can be modulated by its non-consensus ‘head’ sequence but this modulation became not apparent in the evolved R variants. The engineered recombinase variants were found to be active in all recombination reactions tested: excision, integration, and dual recombinase-mediated cassette exchange, dual RMCE. The analysis of the latter reaction catalyzed by the R/TD recombinase pair shows that the condition that supports the most efficient replacement reaction favors efficient TD-mediated integration reaction while favoring efficient R-mediated integration and deletion reactions.