  We develop Standard Model Effective Field Theory (SMEFT) predictions of
$\sigma(\mathcal{G} \,\mathcal{G}\rightarrow h)$, $\Gamma(h \rightarrow
\mathcal{G} \,\mathcal{G})$, $\Gamma(h \rightarrow \mathcal{A} \mathcal{A})$ to
incorporate full two loop Standard Model results at the amplitude level, in
conjunction with dimension eight SMEFT corrections. We simultaneously report
consistent $\Gamma(h \rightarrow \bar{\Psi} {\Psi})$ results including leading
QCD corrections and dimension eight SMEFT corrections. This extends the
predictions of the former processes $\Gamma, \sigma$ to a full set of
corrections at $\mathcal{O}(\bar{v}_T^2/\Lambda^2 (16 \pi^2)^2)$ and
$\mathcal{O}(\bar{v}_T^4/\Lambda^4)$, where $\bar{v}_T$ is the electroweak
scale vacuum expectation value and $\Lambda$ is the cut off scale of the SMEFT.
Throughout, cross consistency between the operator and loop expansions is
maintained by the use of the geometric SMEFT formalism. For $\Gamma(h
\rightarrow \bar{\Psi} {\Psi})$, we include results at
$\mathcal{O}(\bar{v}_T^2/\Lambda^2 (16 \pi^2))$ in the limit where subleading
$m_\Psi \rightarrow 0$ corrections are neglected. We clarify how gauge
invariant SMEFT renormalization counterterms combine with the Standard Model
counter terms in higher order SMEFT calculations when the Background Field
Method is used. We also update the prediction of the total Higgs width in the
SMEFT to consistently include some of these higher order perturbative effects.
