The structure of columnar-jointed lava flows and intrusions has fascinated people for centuries and numerous hypotheses on the mechanisms of formation of columnar jointing have been proposed. In cross-section, weakly developed semicircular internal structures are a near ubiquitous feature of basalt columns. Here we propose a melt-migration model, driven by crystallization and a coeval specific volume decrease inside cooling and solidifying columns, which can explain the observed macroscopic features in columnar-jointed basalts. We study basalts from Hrepphólar (Iceland), combining macroscopic observations, detailed petrography, thermodynamic and rheological modelling of crystallization sequences, and Anisotropy of Magnetic Susceptibility (AMS) of late crystallizing phases (that is, titanomagnetite). These are all consistent with our proposed model, which also suggests that melt-migration features are more likely to develop in certain evolved basaltic lava flows (with early saturation of titanomagnetite), and that the redistribution of melt within individual columns can modify cooling processes.