The effective capacity of communication systems over generalized $κ$-$μ$ shadowed fading channels is investigated in this letter. A novel and analytical expression for the exact effective capacity is derived in terms of extended generalized bivariate Meijer's-$G$ function. To intuitively reveal the impact of the system and channel parameters on the effective capacity, we also derive closed-form expressions for the effective capacity in the asymptotically high signal-to-noise ratio regime. Our results demonstrate that the effective capacity is a monotonically increasing function of channel fading parameters $κ$ and $μ$ as well as the shadowing parameter $m$, while it decays to zero when the delay constraint $θ\rightarrow \infty$.