We present an estimate of the galaxy stellar mass function and its division by morphological type in the local (0.025<z<0.06) Universe. Adopting robust morphological classifications as previously presented (Kelvin et al.) for a sample of 3727 galaxies taken from the Galaxy And Mass Assembly survey, we define a local volume and stellar mass limited sub-sample of 2711 galaxies to a lower stellar mass limit of M= 109.0M⊙. We confirm that the galaxy stellar mass function is well described by a double-Schechter function given by M* = 1010.64M⊙ α1 = -0.43, ϕ*1 = 4.18 dex-1 Mpc-3, α2 = -1.50 and ϕ*2 = 0.74 dex-1 Mpc-3. The constituent morphological-type stellar mass functions are well sampled above our lower stellar mass limit, excepting the faint little blue spheroid population of galaxies. We find approximately 71+3-4 per cent of the stellar mass in the local Universe is found within spheroid dominated galaxies; ellipticals and S0-Sas. The remaining 29+4-3 per cent falls predominantly within late-type disc-dominated systems, Sab-Scds and Sd-Irrs. Adopting reasonable bulgeto-total ratios implies that approximately half the stellar mass today resides in spheroidal structures, and half in disc structures. Within this local sample, we find approximate stellar mass proportions for E: S0-Sa: Sab-Scd: Sd-Irr of 34: 37: 24: 5.