We present the spectroscopic follow-up of the VST Shapley Supercluster Survey (ShaSS). Using the AAOmega fibre-fed spectrograph we have obtained redshifts for >4000 galaxies, selected from 21deg^2 of VST i-band imaging, resulting in a homogenous and highly complete sample of i<18.0 galaxies. The survey area contains eleven X-ray clusters at z=0.05 within the Shapley supercluster, and we use the new redshifts to show how these clusters are all connected within a single coherent structure that entirely fills the 17x17 Mpc^2 region covered by the VST imaging. We show how this dataset permits us to examine the impact of the supercluster environment on galaxies as a function of stellar mass, by providing a large stellar-mass limited sample (>2.7x10^9 Msun) of confirmed supercluster members, each with their local environment characterized in detail.