Understanding how multiple signals are integrated in living cells to produce a balanced response is a major challenge in biology. Two-component signal transduction pathways, such as bacterial chemotaxis, comprise histidine protein kinases (HPKs) and response regulators (RRs). These are used to sense and respond to changes in the environment. Rhodobacter sphaeroides has a complex chemosensory network with two signaling clusters, each containing a HPK, CheA. Here we demonstrate, using a mathematical model, how the outputs of the two signaling clusters may be integrated. We use our mathematical model supported by experimental data to predict that: (1) the main RR controlling flagellar rotation, CheY(6), aided by its specific phosphatase, the bifunctional kinase CheA(3), acts as a phosphate sink for the other RRs, and (2) a phosphorelay pathway involving CheB(2) connects the cytoplasmic cluster kinase CheA(3) with the polar localised kinase CheA(2), and allows CheA(3)-P to phosphorylate non-cognate chemotaxis RRs. These two mechanisms enable the bifunctional kinase/phosphatase activity of CheA(3) to integrate and tune the sensory output of each signaling cluster to produce a balanced response. The signal integration mechanisms identified here may be widely used by other bacteria, since like R. sphaeroides, over 50% of chemotactic bacteria have multiple cheA homologues and need to integrate signals from different sources.