Combining measurements taken using the Wilkinson Microwave Anisotropy Probe (WMAP) from 2001 to 2008 with measurements taken using Planck from 2009 to 2010, we investigate the long-term flux density variability of extragalactic radio sources selected from the Planck Early Release Compact Source Catalogue. The single-year, single-frequency WMAP maps are used to estimate yearly-averaged flux densities of the sources in the four WMAP bands: Ka (33GHz), Q (41GHz), V (61GHz), and W (94GHz). We identify 82, 67, 32, and 15 sources respectively as variable at greater than 99% confidence level in these four bands. The amplitudes of variation are comparable between bands, and are not correlated with either the flux densities or the spectral indices of the sources. The number counts of WMAP Ka-band sources are stable from year to year despite the fluctuation caused by individual source variability. Most of our sources show strong correlation in variability between bands. Almost all the sources that show variability are blazars. We have attempted to fit two simple, four-parameter models to the time-series of 32 sources showing correlated variability at multiple frequencies - a long-term flaring model and a rotating-jet model. We find that 19 sources (60%) can be fit with the simple rotating-jet model, and ten of these also fit the simple long-term flaring model. The remaining 13 sources (40%) show more complex variability behaviour that is not consistent with either model. Extended radio galaxies in our sample show no sign of variability, as expected, with the exception of Pictor A for which we report evidence for a millimetre flare lasting between 2002 and 2010.