The ability to logically engineer novel cellular functions promises a deeper understanding of biological systems. Here we demonstrate the rational design of cellular memory in yeast that employs autoregulatory transcriptional positive feedback. We built a set of transcriptional activators and quantitatively characterized their effects on gene expression in living cells. Modeling in conjunction with the quantitative characterization of the activator-promoter pairs accurately predicts the behavior of the memory network. This study demonstrates the power of taking advantage of components with measured quantitative parameters to specify eukaryotic regulatory networks with desired properties.