Tyrosine site-specific recombinases (SSRs) represent a versatile genome editing tool with considerable therapeutic potential. Recent developments to engineer and evolve SSRs into heterotetramers to improve target site flexibility signified a critical step towards their broad utility in genome editing. However, SSR monomers can form combinations of different homo- and heterotetramers in cells, increasing their off-target potential. Here, we discover that two paired mutations targeting residues implicated in catalysis lead to simple obligate tyrosine SSR systems, where the presence of all distinct subunits to bind as a heterotetramer is obligatory for catalysis. Therefore, only when the paired mutations are applied as single mutations on each recombinase subunit, the engineered SSRs can efficiently recombine the intended target sequence, while the subunits carrying the point mutations expressed in isolation are inactive. We demonstrate the utility of the obligate SSR system to improve recombination specificity of a designer-recombinase for a therapeutic target in human cells. Furthermore, we show that the mutations render the naturally occurring SSRs, Cre and Vika, obligately heteromeric for catalytic proficiency, providing a straight-forward approach to improve their applied properties. These results facilitate the development of safe and effective therapeutic designer-recombinases and advance our mechanistic understanding of SSR catalysis.