Accurate control of a biological process is essential for many critical functions in biology, from the cell cycle to proteome regulation. To achieve this, negative feedback is frequently employed to provide a highly robust and reliable output. Feedback is found throughout biology and technology, but due to challenges posed by its implementation, it is yet to be widely adopted in synthetic biology. In this paper we design a synthetic feedback network using a class of recombinase proteins called integrases, which can be re-engineered to flip the orientation of DNA segments in a digital manner. This system is highly orthogonal, and demonstrates a strong capability for regulating and reducing the expression variability of genes being transcribed under its control. An excisionase protein provides the negative feedback signal to close the loop in this system, by flipping DNA segments in the reverse direction. Our integrase/excisionase negative feedback system thus provides a modular architecture that can be tuned to suit applications throughout synthetic biology and biomanufacturing that require a highly robust and orthogonally controlled output.