We extend our study (Phys. Rev. D 89, 094503 (2014)) of the pion scalar radius in two-flavour lattice QCD to include two additional lattice spacings as well as lighter pion masses, enabling us to perform a combined chiral and continuum extrapolation. We find discretisation artefacts to be small for the radius, and confirm the importance of the disconnected diagrams in reproducing the correct chiral behaviour. Our final result for the scalar radius of the pion at the physical point is ⟨r2⟩πs=0.600±0.052 fm2, corresponding to a value of ℓ¯4=4.54±0.30 for the low-energy constant ℓ¯4 of NLO chiral perturbation theory.