  We investigate the impact of optically induced F\"orster coupling in van der
Waals heterostructures consisting of graphene and a monolayer transition metal
dichalcogenide (TMD). In particular, we predict the corresponding dephasing
rates and a fast energy transfer between the TMD layer and graphene being in
the picosecond range. Exemplary we find a transition rate of thermalized
excitons of about 4 ps$^{-1}$ in a MoSe$_2$-graphene stack at room temperature.
This timescale is in good agreement with the recently measured exciton lifetime
in this heterostructure.
