The construction of atomically precise carbon nanostructures holds promise for developing materials for scientific study and nanotechnology applications. Here, we show that graphene origami is an efficient way to convert graphene into atomically precise, complex nanostructures. By scanning tunneling microscope manipulation at low temperature, we repeatedly fold and unfold graphene nanoislands (GNIs) along an arbitrarily chosen direction. A bilayer graphene stack featuring a tunable twist angle and a tubular edge connection between the layers is formed. Folding single-crystal GNIs creates tubular edges with specified chirality and one-dimensional electronic features similar to those of carbon nanotubes, whereas folding bicrystal GNIs creates well-defined intramolecular junctions. Both origami structural models and electronic band structures are computed to complement analysis of the experimental results. The present atomically precise graphene origami provides a platform for constructing carbon nanostructures with engineered quantum properties and, ultimately, quantum machines.