Protein decay rates are regulated by degradation machinery that clears unnecessary housekeeping proteins and maintains appropriate dynamic resolution for transcriptional regulators. Turnover rates are also crucial for fluorescence reporters that must strike a balance between sufficient fluorescence for signal detection and temporal resolution for tracking dynamic responses. Here, we use components of the Escherichia coli degradation machinery to construct a Saccharomyces cerevisiae strain that allows for tunable degradation of a tagged protein. Using a microfluidic platform tailored for single-cell fluorescence measurements, we monitor protein decay rates after repression using an ssrA-tagged fluorescent reporter. We observe a half-life ranging from 91 to 22 min, depending on the level of activation of the degradation genes. Computational modeling of the underlying set of enzymatic reactions leads to GFP decay curves that are in excellent agreement with the observations, implying that degradation is governed by Michaelis-Menten-type interactions. In addition to providing a reporter with tunable dynamic resolution, our findings set the stage for explorations of the effect of protein degradation on gene regulatory and signalling pathways.