The final results of the search for the lepton flavour violating decay μ^+ →e^+ γ based on the full dataset collected by the MEG experiment at the Paul Scherrer Institut in the period 2009–2013 and totalling 7.5× 10^14 stopped muons on target are presented. No significant excess of events is observed in the dataset with respect to the expected background and a new upper limit on the branching ratio of this decay of ℬ (μ ^+ →e^+ γ ) < 4.2 × 10^-13 (90
