Through their involvement in the integration and excision of a large number of mobile genetic elements, such as phages and integrative and conjugative elements (ICEs), site‐specific recombination systems based on heterobivalent tyrosine recombinases play a major role in genome dynamics and evolution. However, despite hundreds of these systems having been identified in genome databases, very few have been described in detail, with none from phages that infect Bacillota (formerly Firmicutes). In this study, we reanalyzed the recombination module of Lactobacillus delbrueckii subsp. bulgaricus phage mv4, previously considered atypical compared with classical systems. Our results reveal that mv4 integrase is a 369 aa protein with all the structural hallmarks of recombinases from the Tn916 family and that it cooperatively interacts with its recombination sites. Using randomized DNA libraries, NGS sequencing, and other molecular approaches, we show that the 21‐bp core‐attP and attB sites have structural similarities to classical systems only if considering the nucleotide degeneracy, with two 7‐bp inverted regions corresponding to mv4Int core‐binding sites surrounding a 7‐bp strand‐exchange region. We also examined the different compositional constraints in the core‐binding regions, which define the sequence space of permissible recombination sites.