A new model of the L–H transition in tokamaks is proposed, based on the criterion that the transition occurs when plasma turbulence and shear Alfvén waves compete in the vicinity of the last-closed flux surface. The model is used to predict the scaling of the H-mode access power, PL–H, with magnetic and plasma variables. The predictions are in good agreement with the experimental scaling of PL–H with plasma size, density, magnetic field and edge safety factor (plasma current). They are also qualitatively consistent with the dependence of PL–H on ion mass and charge, limiter versus divertor plasmas, single versus double null configurations, the divertor leg length and H–L versus L–H hysteresis. Most notably, the model explains the appearance of the minimum in PL–H with plasma density (in terms of the transition between sheath limited and conduction limited scrape-off layer (SOL) transport) and correctly predicts the scaling of the density minimum with magnetic field and Greenwald number. Finally, the effect of toroidal field reversal is included by making the normalized correlation length of the eddy and maximum safety factor in the edge-SOL layer functions of B ×∇B direction.