Sweet potato feathery mottle virus (SPFMV) and Sweet potato virus C (SPVC) isolates were obtained from sweetpotato shoot or tuberous root samples from three widely separated locations in Australia’s tropical north (Cairns, Darwin, and Kununurra). The samples were planted in the glasshouse and scions obtained from the plants were graft inoculated to Ipomoea setosa plants. Virus symptoms were recorded in the field in Kununurra and in glasshouse-grown sweetpotato and I. setosa plants. RNA extracts from I. setosa leaf samples were subjected to high-throughput sequencing. New complete SPFMV (n = 17) and SPVC (n = 6) genomic sequences were obtained and compared with 47 sequences from GenBank. Phylogenetic analysis revealed that the 17 new SPFMV genomes all fitted within either major phylogroup A, minor phylogroup II, formerly O; or major phylogroup B, formerly RC. Major phylogroup A’s minor phylogroup I, formerly EA, only appeared when recombinants were included. Numbers of SPVC genomes were insufficient to subdivide it into phylogroups. Within phylogroup A’s minor phylogroup II, the closest genetic match between an Australian and a Southeast Asian SPFMV sequence was the 97.4% nucleotide identity with an East Timorese sequence. Recombination analysis of the 43 SPFMV and 27 SPVC sequences revealed evidence of 44 recombination events, 16 of which involved interspecies sequence transfers between SPFMV and SPVC and 28 intraspecies transfers, 17 in SPFMV and 11 in SPVC. Within SPFMV, 11 intraspecies recombination events were between different major phylogroups and 6 were between members of the same major phylogroup. Phylogenetic analysis accounting for the detected recombination events within SPFMV sequences yielded evidence of minor phylogroup II and phylogroup B but the five sequences from minor phylogroup I were distributed in two separate groups among the sequences of minor phylogroup II. For the SPVC sequences, phylogenetic analysis accounting for the detected recombination events revealed three major phylogroups (A, B, and C), with major phylogroup A being further subdivided into two minor phylogroups. Within the recombinant genomes of both viruses, their PI, NIa-Pro, NIb, and CP genes contained the highest numbers of recombination breakpoints. The high frequency of interspecies and inter-phylogroup recombination events reflects the widespread occurrence of mixed SPVC and SPFMV infections within sweetpotato plants. The prevalence of infection in northern Australian sweetpotato samples reinforces the need for improved virus testing in healthy sweetpotato stock programs. Furthermore, evidence of genetic connectivity between Australian and East Timorese SPFMV genomes emphasizes the need for improved biosecurity measures to protect against potentially damaging international virus movements.