Although oscillatory circuits are prevalent in transcriptional regulation, it is unclear how a circuit's structure and the specific parameters that describe its components determine the shape of its oscillations. Here, we engineer a minimal, inducible human nuclear factor κB (NF-κB)-based system that is composed of NF-κB (RelA) and degradable inhibitor of NF-κB (IκBα), into the yeast, Saccharomyces cerevisiae. We define an oscillation's waveform quantitatively as a function of signal amplitude, rest time, rise time, and decay time; by systematically tuning RelA concentration, the strength of negative feedback, and the degradation rate of IκBα, we demonstrate that peak shape and frequency of oscillations can be controlled in vivo and predicted mathematically. In addition, we show that nested negative feedback loops can be employed to specifically tune the frequency of oscillations while leaving their peak shape unchanged. In total, this work establishes design principles that enable function-guided design of oscillatory signaling controllers in diverse synthetic biology applications.