Rewiring signaling networks imparts cells with new functionalities that are useful for engineering cell therapies and directing cell development. While much effort has gone into connecting extracellular inputs to desired outputs, less has been done to control the signal processing steps in-between. Here, we develop synthetic signal processing circuits in mammalian cells using proteins derived from bacterial two-component signaling pathways. First, we isolate kinase and phosphatase activities from the bifunctional histidine kinase EnvZ and demonstrate tunable phosphorylation control of the response regulator OmpR via simultaneous phosphoregulation by an EnvZ kinase and phosphatase. We show that modulation of phosphatase expression at the mRNA and protein levels via miRNAs and small molecule-regulated degradation domains, respectively, can effectively tune kinase-to-output responses. Further, we implement a novel phosphorylation-based miRNA sensor that effectively classifies cell types and enables cell type-specific kinase-output signaling responses. Finally, we implement a tunable negative feedback controller by co-expressing the kinase-driven output gene with the small molecule-tunable phosphatase, substantially reducing both gene expression noise and sensitivity to perturbations at the transcriptional and translational level. Our work lays the foundation for establishing tunable, precise, and robust control over cell behavior with synthetic signaling networks.