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During tissue development, patterns of gene expression determine the spatial arrangement of cell types. In many cases, gradients of secreted signalling molecules-morphogens-guide this process by controlling downstream transcriptional networks. A mechanism commonly used in these networks to convert the continuous information provided by the gradient into discrete transitions between adjacent cell types is the genetic toggle switch, composed of cross-repressing transcriptional determinants. Previous analyses have emphasised the steady state output of these mechanisms. Here, we explore the dynamics of the toggle switch and use exact numerical simulations of the kinetic reactions, the corresponding Chemical Langevin Equation, and Minimum Action Path theory to establish a framework for studying the effect of gene expression noise on patterning time and boundary position. This provides insight into the time scale, gene expression trajectories and directionality of stochastic switching events between cell states. Taking gene expression noise into account predicts that the final boundary position of a morphogen-induced toggle switch, although robust to changes in the details of the noise, is distinct from that of the deterministic system. Moreover, the dramatic increase in patterning time close to the boundary predicted from the deterministic case is substantially reduced. The resulting stochastic switching introduces differences in patterning time along the morphogen gradient that result in a patterning wave propagating away from the morphogen source with a velocity determined by the intrinsic noise. The wave sharpens and slows as it advances and may never reach steady state in a biologically relevant time. This could explain experimentally observed dynamics of pattern formation. Together the analysis reveals the importance of dynamical transients for understanding morphogen-driven transcriptional networks and indicates that gene expression noise can qualitatively alter developmental patterning.