Higgs boson properties are studied in the fourlepton decay channel (where lepton = e, mu) using 139 fb(-1) of proton-proton collision data recorded at v s =13 TeV by the ATLAS experiment at the Large Hadron Collider. The inclusive cross-section times branching ratio for H -> ZZ * decay is measured to be 1.34 +/- 0.12 pb for a Higgs boson with absolute rapidity below 2.5, in good agreement with the Standard Model prediction of 1.33 +/- 0.08 pb. Crosssections times branching ratio are measured for the main Higgs boson production modes in several exclusive phasespace regions. The measurements are interpreted in terms of coupling modifiers and of the tensor structure of Higgs boson interactions using an effective field theory approach. Exclusion limits are set on the CP-even and CP-odd `beyond the Standard Model' couplings of the Higgs boson to vector bosons, gluons and top quarks.