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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 $\log[M_{\rm{BH}}/M_{\odot}] = 8.0 \pm 0.6$ (1$σ$ uncertainties). This is in good agreement with previous estimates based on the H$α$ and H$β$ 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 ($v_{\rm{out}} \lesssim 0.03c$), implying these are unlikely to drive significant galaxy-scale AGN feedback.