  The calculation of the leading electroweak corrections to physical transition
matrix elements in powers of $M_H^2/v^2$ can be greatly simplified in the limit
$M_H^2\gg M_W^2,\, M_Z^2$ through the use of the Goldstone boson equivalence
theorem. This theorem allows the vector bosons $W^\pm$ and $Z$ to be replaced
by the associated scalar Goldstone bosons $w^\pm$, $z$ which appear in the
symmetry breaking sector of the Standard Model in the limit of vanishing gauge
couplings. In the present paper, we extend the equivalence theorem
systematically to include the Yukawa interactions between the fermions and the
Higgs and Goldstone bosons of the Standard Model. The corresponding Lagrangian
${\cal L}_{EQT}$ is given, and is formally renormalized to all orders. The
renormalization conditions are formulated both to make connection with physical
observables and to satisfy the requirements underlying the equivalence theorem.
As an application of this framework, we calculate the dominant radiative
corrections to fermionic Higgs decays at one loop including the virtual effects
of a heavy top quark. We apply the result to the decays $H\rightarrow t\bar{t}$
and $H\rightarrow b\bar{b}$, and find that the equivalence theorem results
including fermions are quite accurate numerically for Higgs-boson masses $M_H>
400\,(350)$ GeV, respectively, even for $m_t=175$ GeV.
