  We report the direct observation of intervalley exciton between the Q
conduction valley and $\Gamma$ valence valley in bilayer WSe$_2$ by
photoluminescence. The Q$\Gamma$ exciton lies at ~18 meV below the QK exciton
and dominates the luminescence of bilayer WSe$_2$. By measuring the exciton
spectra at gate-tunable electric field, we reveal different interlayer electric
dipole moments and Stark shifts between Q$\Gamma$ and QK excitons. Notably, we
can use the electric field to switch the energy order and dominant luminescence
between Q$\Gamma$ and QK excitons. Both Q$\Gamma$ and QK excitons exhibit
pronounced phonon replicas, in which two-phonon replicas outshine the
one-phonon replicas due to the existence of (nearly) resonant exciton-phonon
scatterings and numerous two-phonon scattering paths. We can simulate the
replica spectra by comprehensive theoretical modeling and calculations. The
good agreement between theory and experiment for the Stark shifts and phonon
replicas strongly supports our assignment of Q$\Gamma$ and QK excitons.
