The last missing correction to the muon lifetime in the Standard Model
at ${\cal O}(\alpha^2)$ coming from gauge and Higgs boson loops is
presented. The associated contribution to the parameter $\Delta r$ in
the on-shell scheme ranges from $6 \times 10^{-5}$ to $-4 \times
10^{-5}$ for Higgs boson masses from 100~GeV to 1~TeV. This result
translates into a shift of the $W$ boson mass which does not exceed
$\pm 1$~MeV in the same range and amounts in particular to
approximately $- 0.8$~MeV for a 115~GeV Higgs boson.
