We present results from the spectral fitting of the candidate black hole X-ray binary Swift J1753.5-0127 in an accretion state previously unseen in this source. We fit the 0.7-78 keV spectrum with a number of models, however the preferred model is one of a multi-temperature disk with an inner disk temperature kT in = 0.252±0.003 keV scattered into a steep power-law with photon index Γ = 6.39 +0.08 −0.02 and an additional hard power law tail (Γ = 1.79 ± 0.02). We report on the emergence of a strong disk-dominated component in the X-ray spectrum and we conclude that the source has entered the soft state for the first time in its ∼10 year prolonged outburst. Using reasonable estimates for the distance to the source (3 kpc) and black hole mass (5M ⊙ ), we find the unabsorbed luminosity (0.1-100 keV) to be ≈ 0.60% of the Eddington luminosity, making this one of the lowest luminosity soft states recorded in X-ray binaries. We also find that the accretion disk extended towards the compact object during its transition from hard to soft, with the inner radius estimated to be R in = 28.0 +0.7 −0.4 R g or ∼ 12R g , dependent on the boundary condition chosen, assuming the above distance and mass, a spectral hardening factor f = 1.7 and a binary inclination i = 55• .