Overlap-directed DNA assembly methods allow multiple DNA parts to be assembled together in one reaction. These methods, which rely on sequence homology between the ends of DNA parts, have become widely adopted in synthetic biology, despite being incompatible with a key principle of engineering: modularity. To answer this, we present MODAL: a Modular Overlap-Directed Assembly with Linkers strategy that brings modularity to overlap-directed methods, allowing assembly of an initial set of DNA parts into a variety of arrangements in one-pot reactions. MODAL is accompanied by a custom software tool that designs overlap linkers to guide assembly, allowing parts to be assembled in any specified order and orientation. The in silico design of synthetic orthogonal overlapping junctions allows for much greater efficiency in DNA assembly for a variety of different methods compared with using non-designed sequence. In tests with three different assembly technologies, the MODAL strategy gives assembly of both yeast and bacterial plasmids, composed of up to five DNA parts in the kilobase range with efficiencies of between 75 and 100%. It also seamlessly allows mutagenesis to be performed on any specified DNA parts during the process, allowing the one-step creation of construct libraries valuable for synthetic biology applications.