Perception, cognition and behavior rely on flexible communication between microcircuits in distinct cortical regions. The mechanisms underlying rapid information rerouting between such microcircuits are still unknown. It has been proposed that changing patterns of coherence between local gamma rhythms support flexible information rerouting. The stochastic and transient nature of gamma oscillations in vivo, however, is hard to reconcile with such a function. Here we show that models of cortical circuits near the onset of oscillatory synchrony selectively route input signals despite the short duration of gamma bursts and the irregularity of neuronal firing. In canonical multiarea circuits, we find that gamma bursts spontaneously arise with matched timing and frequency and that they organize information flow by large-scale routing states. Specific self-organized routing states can be induced by minor modulations of background activity.