An isothermal, single-reaction protocol for assembling multiple, overlapping DNA molecules by the concerted action of a 5’-exonuclease, a DNA polymerase, and a DNA ligase is described. The DNA fragments are first recessed to produce ssDNA overhangs that are specifically annealed, and then they are covalently joined. This assembly protocol can be used to seamlessly construct synthetic and natural genes, genetic pathways, and entire genomes. This method could be a very useful molecular engineering tool.