This article provides a knowledge-based and energy-centred unified growth model of the transition from limited to sustained economic growth. We model the transition between: (i) a pre-modern organic regime defined by limited growth in per capita output, high fertility, low levels of human capital, technical change generated by learning-by-doing, and rare general purpose technology (GPT) arrivals; and (ii) a modern fossil regime characterized by sustained growth in per capita output, low fertility, high levels of human capital, technical change generated by profit-motivated R&D, and increasingly frequent GPT arrivals. The associated energy transition re- sults from the endogenous shortage in the availability of renewable resources, and the arrival of new GPTs that, together, redirect technical change towards the exploitation of previously unprofitable exhaustible energy. A calibrated version of the model replicates the historical experience of Great Britain from 1700 to 1960. Counterfactual simulations are performed to characterize the impact of the energy transition on the timing and magnitude of the British economic take-off. Another simulation exercise compares the different trajectories of Western Europe and Eastern Asia to determine which parameters of our model are the most crucial to reflect the diverging dynamics of these two world regions.