Palaeomagnetic apparent polar wander (APW) paths from the world's cratons at 1300–700 Ma can constrain the palaeogeographic possibilities for a long-lived and all-inclusive Rodinia supercontinent. Laurentia's APW path is the most complete and forms the basis for superposition by other cratons' APW paths to identify possible durations of those cratons' inclusion in Rodinia, and also to generate reconstructions that are constrained both in latitude and longitude relative to Laurentia. Baltica reconstructs adjacent to the SE margin of Greenland, in a standard and geographically ‘upright’ position, between c. 1050 and 600 Ma. Australia reconstructs adjacent to the pre-Caspian margin of Baltica, geographically ‘inverted’ such that cratonic portions of Queensland are juxtaposed with that margin via collision at c. 1100 Ma. Arctic North America reconstructs opposite to the CONgo+São Francisco craton at its DAmaride–Lufilian margin (the ‘ANACONDA’ fit) throughout the interval 1235–755 Ma according to palaeomagnetic poles of those ages from both cratons, and the reconstruction was probably established during the c. 1600–1500 Ma collision. Kalahari lies adjacent to Mawsonland following collision at c. 1200 Ma; the Albany–Fraser orogen continues along-strike to the Sinclair-Kwando-Choma-Kaloma belt of south-central Africa. India, South China and Tarim are in proximity to Western Australia as previously proposed; some of these connections are as old as Palaeoproterozoic whereas others were established at c. 1000 Ma. Siberia contains a succession of mainly sedimentary-derived palaeomagnetic poles with poor age constraints; superposition with the Keweenawan track of the Laurentian APW path produces a position adjacent to western India that could have persisted from Palaeoproterozoic time, along with North China according to its even more poorly dated palaeomagnetic poles. The Amazonia, West Africa and Rio de la Plata cratons are not well constrained by palaeomagnetic data, but they are placed in proximity to western Laurentia. Rift successions of c. 700 Ma in the North American COrdillera and BRAsiliano-Pharuside orogens indicate breakup of these ‘COBRA’ connections that existed for more than one billion years, following Palaeoproterozoic accretionary assembly. The late Neoproterozoic transition from Rodinia to Gondwanaland involved rifting events that are recorded on many cratons through the interval c. 800–700 Ma and collisions from c. 650–500 Ma. The pattern of supercontinental transition involved large-scale dextral motion by West Africa and Amazonia, and sinistral motion plus rotation by Kalahari, Australia, India and South China, in a combination of introverted and extroverted styles of motion. The Rodinia model presented here is a marked departure from standard models, which have accommodated recent discordant palaeomagnetic data either by excluding cratons from Rodinia altogether, or by decreasing duration of the supercontinental assembly. I propose that the revised model herein is the only possible long-lived solution to an all-encompassing Rodinia that viably accords with existing palaeomagnetic data.