Thermal annealing is usually needed to direct the assembly of multiple complementary DNA strands into desired entities. We show that, with a magnesium-free buffer containing NaCl, complex cocktails of DNA strands and proteins can self-assemble isothermally, at room or physiological temperature, into user-defined nanostructures, such as DNA origamis, single-stranded tile assemblies and nanogrids. In situ, time-resolved observation reveals that this self-assembly is thermodynamically controlled, proceeds through multiple folding pathways and leads to highly reconfigurable nanostructures. It allows a given system to self-select its most stable shape in a large pool of competitive DNA strands. Strikingly, upon the appearance of a new energy minimum, DNA origamis isothermally shift from one initially stable shape to a radically different one, by massive exchange of their constitutive staple strands. This method expands the repertoire of shapes and functions attainable by isothermal self-assembly and creates a basis for adaptive nanomachines and nanostructure discovery by evolution.