Dynamic strain ageing (DSA) is the phenomenon in which solute atoms diffuse around dislocations and retard dislocation motion, leading to negative strain-rate sensitivity (nSRS) and thus to material instabilities during processing, an important issue in commercial metal alloys. Here, we show the mechanism of DSA and nSRS on experimental strain-rate, temperature and stress scales for Al-Mg to be single-atomic-hop motion of solutes from the compression to the tension side of a dislocation core. We derive an analytic expression for the strengthening versus strain rate and temperature that justifies widely used phenomenological forms, provides specific dependences of the parameters on material properties and is supported by atomistic kinetic Monte Carlo simulations. Using literature material properties, the predicted strengthening quantitatively agrees with the experimentally derived behaviour of Al-2.5% Mg at 300K, and qualitatively agrees with the strain rate and temperature ranges of DSA and nSRS in Al-Mg alloys. The analyses herein show a clear path for multiscale design, from quantum to continuum mechanics, of solute strengthening in face-centred-cubic metal alloys.