We present new broadband X-ray observations of the type-I Seyfert galaxy IRAS 09149–6206, taken in 2018 with XMM-Newton, NuSTAR and Swift. The source is highly complex, showing a classic ‘warm’ X-ray absorber, additional absorption from highly ionised iron, strong relativistic reflection from the innermost accretion disc and further reprocessing by more distant material. By combining X-ray timing and spectroscopy, we have been able to fully characterise the supermassive black hole in this system, constraining both its mass and – for the first time – its spin. The mass is primarily determined by X-ray timing constraints on the break frequency seen in the power spectrum, and is found to be log [MBH/M⊙] = 8.0 ± 0.6 (1σ uncertainties). This is in good agreement with previous estimates based on the Hα and Hβ line widths, and implies that IRAS 09149–6206 is radiating at close to (but still below) its Eddington luminosity. The spin is constrained via detailed modelling of the relativistic reflection, and is found to be $a^* = 0.94^{+0.02}_{-0.07}$ (90% confidence), adding IRAS 09149–6206 to the growing list of radio-quiet AGN that host rapidly rotating black holes. The outflow velocities of the various absorption components are all relatively modest (vout ≲ 0.03c), implying these are unlikely to drive significant galaxy-scale AGN feedback.