A search is presented for a standard model-like Higgs boson decaying to the μ+μ− or e+e− final states based on proton–proton collisions recorded by the CMS experiment at the CERN LHC. The data correspond to integrated luminosities of 5.0 fb−1 at a centre-of-mass energy of 7 TeV and 19.7 fb−1 at 8 TeV for the μ+μ− search, and of 19.7 fb−1 at 8 TeV for the e+e− search. Upper limits on the production cross section times branching fraction at the 95% confidence level are reported for Higgs boson masses in the range from 120 to 150 GeV. For a Higgs boson with a mass of 125 GeV decaying to μ+μ−, the observed (expected) upper limit on the production rate is found to be 7.4 (6.5−1.9+2.8) times the standard model value. This corresponds to an upper limit on the branching fraction of 0.0016. Similarly, for e+e−, an upper limit of 0.0019 is placed on the branching fraction, which is ≈3.7×105 times the standard model value. These results, together with recent evidence of the 125 GeV boson coupling to τ-leptons with a larger branching fraction consistent with the standard model, confirm that the leptonic couplings of the new boson are not flavour-universal.