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.
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