Scaffolded DNA origami is a widely used technology for self-assembling precisely structured nanoscale objects that contain a large number of addressable features. Typical scaffolds are long, single strands of DNA (ssDNA) that are folded into distinct shapes through the action of many, short ssDNA staples that are complementary to several different domains of the scaffold. However, sources of long single-stranded DNA are scarce, limiting the size and complexity of structures that can be assembled. Here we demonstrated that dsDNA (double-stranded DNA) scaffolds can be directly used to fabricate integrated DNA origami structures that incorporate both of the constituent ssDNA molecules. Two basic principles were employed in the design of scaffold folding paths: folding path asymmetry and periodic convergence of the two ssDNA scaffold strands. Asymmetry in the folding path minimizes unwanted complementarity between staples, and incorporating an offset between the folding paths of each ssDNA scaffold strand reduces the number of times that complementary portions of the strands are brought into close proximity with one another, both of which decrease the likelihood of dsDNA scaffold recovery. Meanwhile, the folding paths of the two ssDNA scaffold strands were designed to periodically converge to promote the assembly of a single, unified structure rather than two individual ones. Our results reveal that this basic strategy can be used to reliably assemble integrated DNA nanostructures from dsDNA scaffolds.