Studies of the spin, parity and tensor couplings of the Higgs boson in the H -> ZZ* -> 4l, H -> WW* -> e nu mu nu and H -> gamma gamma decay processes at the LHC are presented. The investigations are based on 25 fb(-1) of pp collision data collected by the ATLAS experiment at root s = 7 TeV and root s = 8 TeV. The Standard Model (SM) Higgs boson hypothesis, corresponding to the quantum numbers J (P) = 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* -> e nu mu nu. 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.