  Using the general notions of Batalin, Fradkin, Fradkina and Tyutin to convert
second class systems into first class ones, we present a gauge invariant
formulation of the massive Yang-Mills theory by embedding it in an extended
phase space. The infinite set of correction terms necessary for obtaining the
involutive constraints and Hamiltonian is explicitly computed and expressed in
a closed form. It is also shown that the extra fields introduced in the
correction terms are exactly identified with the auxiliary scalars used in the
generalized St\"uckelberg formalism for converting a gauge noninvariant
Lagrangian into a gauge invariant form.
