The begomoviruses (BGVs) are plant pathogens that evolved in the Old World during the Cretaceous and arrived to the New World (NW) in the Cenozoic era. A subgroup of NW BGVs, the “Squash leaf curl virus (SLCV) lineage” (S-Lin), includes viruses with unique characteristics. To get clues on the evolutionary origin of this lineage, a search for divergent members was undertaken. Four novel BGVs were characterized, including one that is basal to the group. Comparative analyses led to discover a ~670 bp genome module that is nearly exclusive of this lineage, encompassing the replication origin, the AC4 gene, and 480 bp of the Rep gene. A similar DNA module was found in two curtoviruses, hence suggesting that the S-Lin ancestor acquired its distinctive genomic segment by recombination with a curtovirus. This hypothesis was definitely disproved by an in-depth sequence analysis. The search for homologs of S-Lin Rep uncover the common origin of Rep proteins encoded by diverse Geminiviridae genera and viral “fossils” integrated at plant genomes. In contrast, no homolog of S-Lin Rep was found in public databases. Consequently, it was concluded that the SLCV clade ancestor evolved by a recombination event between a primitive NW BGV and a virus from a hitherto unknown lineage.