Studies of the spin, parity and tensor couplings of the Higgs boson in the H→ZZ∗→4ℓ, H→WW∗→eνμν and H→γγ decay processes at the LHC are presented. The investigations are based on 25fb−1 of pp collision data collected by the ATLAS experiment at √s=7 TeV and √s=8 TeV. The Standard Model (SM) Higgs boson hypothesis, corresponding to the quantum numbers JP=0+, is tested against several alternative spin scenarios, including non-SM spin-0 and spin-2 models with universal and non-universal couplings to fermions and vector bosons. All tested alternative models are excluded in favour of the SM Higgs boson hypothesis at more than 99.9 % confidence level. Using the H→ZZ∗→4ℓ and H→WW∗→eνμν decays, the tensor structure of the interaction between the spin-0 boson and the SM vector bosons is also investigated. The observed distributions of variables sensitive to the non-SM tensor couplings are compatible with the SM predictions and constraints on the non-SM couplings are derived.