We report here the annotation of the complete genomes of four novel lytic Staphylococcus phages; Stab20, Stab21, Stab22 and Stab23. These phages have double-stranded DNA genomes ranging between 153,338 and 155,962 bp in size with terminal repeats of 10,814-12,304 bp. The genome analysis suggests that they represent new phage species within the genus Kayvirus in the subfamily Twortvirinae of the family Herelleviridae.