  The existence of a Seshadri stratification on an embedded projective variety
provides a flat degeneration of the variety to a union of projective toric
varieties, called a semi-toric variety. Such a stratification is said to be
normal when each irreducible component of the semi-toric variety is a normal
toric variety. In this case, we show that a Gr\"obner basis of the defining
ideal of the semi-toric variety can be lifted to define the embedded projective
variety. Applications to Koszul and Gorenstein properties are discussed.
