Models of X-ray reverberation from extended coronae are developed from general relativistic ray tracing simulations. Reverberation lags between correlated variability in the directly observed continuum emission and that reflected from the accretion disc arise due to the additional light travel time between the corona and reflecting disc. X-ray reverberation is detected from an increasing sample of Seyfert galaxies and a number of common properties are observed, including a transition from the characteristic reverberation signature at high frequencies to a hard lag within the continuum component at low frequencies, as well as a pronounced dip in the reverberation lag at 3 keV. These features are not trivially explained by the reverberation of X-rays originating from simple point sources. We therefore model reverberation from coronae extended both over the surface of the disc and vertically. Causal propagation through its extent for both the simple case of constant velocity propagation and propagation linked to the viscous time-scale in the underlying accretion disc is included as well as stochastic variability arising due to turbulence locally on the disc. We find that the observed features of X-ray reverberation in Seyfert galaxies can be explained if the long time-scale variability is dominated by the viscous propagation of fluctuations through the corona. The corona extends radially at low height over the surface of the disc but with a bright central region in which fluctuations propagate up the black hole rotation axis driven by more rapid variability arising from the innermost regions of the accretion flow.