An exotic narrow state in the D0D0π + mass spectrum just below the D∗+D0 mass threshold is studied using a data set corresponding to an integrated luminosity of 9 fb−1 acquired with the LHCb detector in proton-proton collisions at centre-of-mass energies of 7, 8 and 13 TeV. The state is consistent with the ground isoscalar T+ cc tetraquark with a quark content of ccud and spin-parity quantum numbers JP = 1+. Study of the DD mass spectra disfavours interpretation of the resonance as the isovector state. The decay structure via intermediate off-shell D∗+ mesons is confirmed by the D0π + mass distribution. The mass of the resonance and its coupling to the D∗D system are analysed. Resonance parameters including the pole position, scattering length, effective range and compositeness are measured to reveal important information about the nature of the T+ cc state. In addition, an unexpected dependence of the production rate on track multiplicity is observed.