Studies of the spin and parity quantum numbers of the Higgs boson are presented, based on proton–proton collision data collected by the ATLAS experiment at the LHC. The Standard Model spin–parity JP=0+JP=0+ hypothesis is compared with alternative hypotheses using the Higgs boson decays H→γγH→γγ, H→ZZ⁎→4ℓH→ZZ⁎→4ℓ and H→WW⁎→ℓνℓνH→WW⁎→ℓνℓν, as well as the combination of these channels. The analysed dataset corresponds to an integrated luminosity of 20.7 fb−1 collected at a centre-of-mass energy of √s=8TeV. For the H→ZZ⁎→4ℓH→ZZ⁎→4ℓ decay mode the dataset corresponding to an integrated luminosity of 4.6 fb−1 collected at √s=7TeV is included. The data are compatible with the Standard Model JP=0+JP=0+ quantum numbers for the Higgs boson, whereas all alternative hypotheses studied in this Letter, namely some specific JP=0−,1+,1−,2+JP=0−,1+,1−,2+ models, are excluded at confidence levels above 97.8%. This exclusion holds independently of the assumptions on the coupling strengths to the Standard Model particles and in the case of the JP=2+JP=2+ model, of the relative fractions of gluon-fusion and quark–antiquark production of the spin-2 particle. The data thus provide evidence for the spin-0 nature of the Higgs boson, with positive parity being strongly preferred