With each cell division of phytoplankton, the newly established cell wall surface is immediately colonized by environmental bacteria, yet phytoplankton microbiomes are often highly specific. While phytoplankton-bacteria interactions play fundamental roles in marine ecosystems, namely for primary production, we have little understanding of the ecological paradigms behind epiphytic microbiome assembly. In a chance recolonization experiment, we exposed axenic diatoms of Thalassiosira rotula to several complex and compositionally different bacterial inocula obtained from conspecific, heterospecific and congeneric diatoms. The resulting microbiomes revealed a convergent assembly of highly diverse and compositionally different bacterial inocula containing up to 4406 operational taxonomic units (OTU) towards a consistent and reproducible T. rotula core microbiome consisting of 27 OTU, accounting for a total relative abundance of 94 +/- 4%. The microbiomes were dominated by Rhodobacteraceae (30.5%), Alteromonadaceae (27.7%), Oceanospirillales (18.5%) and were quantitatively most similar to its conspecific original. The high degree of overlap among the same OTU shared across the T. rotula acceptor microbiomes was indicative of a highly confined, stable and reproducible core microbiome. These observations reject bacterial colonization due to lottery theory and suggest a habitat filtering, niche-based microbiome assembly on the cosmopolitan marine bloom forming diatom T. rotula.