  The deviation of the measured value of the muon anomalous magnetic moment
from the standard model prediction can be completely explained by mixing of the
muon with extra vectorlike leptons, L and E, near the electroweak scale. This
mixing simultaneously contributes to the muon mass. We show that the
correlation between contributions to the muon mass and muon g-2 is controlled
by the mass of the neutrino originating from the doublet L. Positive
correlation, simultaneously explaining both measured values, requires this mass
below 200 GeV. The decay rate of the Higgs boson to muon pairs is modified and,
in the region of the parameter space that can explain the muon anomalous
magnetic moment within one standard deviation, it ranges from 0.5 to 24 times
the standard model prediction. In the same scenario, $h \to \gamma \gamma$ can
be enhanced or lowered by ~50% from the standard model prediction. The
explanation of the muon g-2 anomaly and predictions for $h \to \gamma \gamma$
are not correlated since these are controlled by independent parameters. This
scenario can be embedded in a model with three complete vectorlike families
featuring gauge coupling unification, sufficiently stable proton, and the Higgs
quartic coupling remaining positive all the way to the grand unification scale.
