A highly accurate, fully analytic solution for the continuous wave and the probe wave in Brillouin amplification, in lossless optical fibers, is given. It is experimentally confirmed that the reported analytic solution can account for spectral distortion and pump depletion in the parameter space that is relevant to Brillouin fiber sensor applications, as well as applications in photonic logic. The analytic solutions are valid characterizations of Brillouin amplification in both the low and high nonlinearity regime, for short fiber lengths.