Higgs boson properties are studied in the four-lepton decay channel (where lepton = e, $\mu $) using 139 $\hbox {fb}^{-1}$ of proton–proton collision data recorded at $\sqrt{s}=$13 TeV by the ATLAS experiment at the Large Hadron Collider. The inclusive cross-section times branching ratio for $H\rightarrow ZZ^*$ decay is measured to be $1.34 \pm 0.12$ pb for a Higgs boson with absolute rapidity below 2.5, in good agreement with the Standard Model prediction of $1.33 \pm 0.08$ pb. Cross-sections times branching ratio are measured for the main Higgs boson production modes in several exclusive phase-space 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.