NGC 1566 is a changing-look active galaxy that exhibited an outburst during 2017-2018 with a peak in June 2018. We triggered AstroSat observations of NGC 1566 twice in August and October 2018 during its declining phase. Using the AstroSat observations along-with two XMM-Newton observations in 2015 (pre-outburst) and June 2018 (peak-outburst), we found that the X-ray power-law, the soft X-ray excess, and the disk components showed extreme variability during the outburst. Especially, the soft excess was negligible in 2015 before the outburst, it increased to a maximum level by a factor of > 200 in June 2018, and reduced dramatically by a factor of ∼ 7.4 in August 2018 and become undetectable in October 2018. The Eddington fraction (L/L Edd ) increased from ∼ 0.1% (2015) to ∼ 5% (June 2018), then decreased to ∼ 1.5% (August 2018) and 0.3% (October 2018). Thus, NGC 1566 made a spectral transition from a high soft-excess state to a negligible soft-excess state at a few % of the Eddington rate. The soft-excess is consistent with warm Comptonization in the inner disk that appears to have developed during the outburst and disappeared towards the end of the outburst over a timescale comparable to the sound crossing time. The multi-wavelength spectral evolution of NGC 1566 during the outburst is most likely caused by the radiation pressure instability in the inner regions of the accretion disk in NGC 1566.