Protein function is typically studied and engineered by modulating protein levels within the complex cellular environment. To achieve fast, targeted, and predictable control of cellular protein levels without genetic manipulation of the target, we developed a technology for post-translational depletion based on a bifunctional molecule (NanoDeg) consisting of the antigen-binding fragment from the Camelidae species heavy-chain antibody (nanobody) fused to a degron signal that mediates degradation through the proteasome. We provide proof-of-principle demonstration of targeted degradation using a nanobody against the green fluorescent protein (GFP). Guided by predictive modeling, we show that customizing the NanoDeg rate of synthesis, rate of degradation, and mode of degradation enables quantitative and predictable control over the target's levels. Integrating the GFP-specific NanoDeg within a genetic circuit based on stimulus-dependent GFP output results in enhanced dynamic range and resolution of the output signal. By providing predictable control over cellular proteins' levels, the NanoDeg system could be readily used for a variety of systems-level analyses of cellular protein function.