Cellular metagenomes are primarily used for investigating microbial community structure and function. However, cloned fosmids from such metagenomes capture phage genome fragments that can be used as a source of phage genomes. We show that fosmid cloning from cellular metagenomes and sequencing at a high coverage is a credible alternative to constructing metaviriomes and allows capturing and assembling novel, complete phage genomes. It is likely that phages recovered from cellular metagenomes are those replicating within cells during sample collection and represent "active" phages, naturally amplifying their genomic DNA and increasing chances for cloning. We describe five sets of siphoviral contigs (MEDS1, MEDS2, MEDS3, MEDS4, and MEDS5), obtained by sequencing fosmids from the cellular metagenome of the deep chlorophyll maximum in the Mediterranean. Three of these represent complete siphoviral genomes and two represent partial ones. This is the first set of phage genomes assembled directly from cellular metagenomic fosmid libraries. They exhibit low sequence similarities to one another and to known siphoviruses but are remarkably similar in overall genome architecture. We present evidence suggesting they infect picocyanobacteria, likely Synechococcus. Four of these sets also define a novel branch in the phylogenetic tree of phage large subunit terminases. Moreover, some of these siphoviral groups are globally distributed and abundant in the oceans, comparable to some known myoviruses and podoviruses. This suggests that, as more siphoviral genomes become available, we will be better able to assess the abundance and influence of this diverse and polyphyletic group in the marine habitat.