We present the evolution of galaxy sizes, from redshift 2 to 0, for actively star forming and passive galaxies in the cosmological hydrodynamical 100 super( 3) cMpc3 simulation of the EAGLE project. We find that the sizes increase with stellar mass, but that the relation weakens with increasing redshift. Separating galaxies by their star formation activity, we find that passive galaxies are typically smaller than active galaxies at a fixed stellar mass. These trends are consistent with those found in observations and the level of agreement between the predicted and observed size-mass relations is of the order of 0.1 dex for z < 1 and 0.2-0.3 dex from redshift 1 to 2. We use the simulation to compare the evolution of individual galaxies with that of the population as a whole. While the evolution of the size-stellar mass relation for active galaxies provides a good proxy for the evolution of individual galaxies, the evolution of individual passive galaxies is not well represented by the observed size-mass relation due to the evolving number density of passive galaxies. Observations of z ~ 2 galaxies have revealed an abundance of massive red compact galaxies, which depletes below z ~ 1. We find that a similar population forms naturally in the simulation. Comparing these galaxies with their z = 0 descendants, we find that all compact galaxies grow in size due to the high-redshift stars migrating outwards. Approximately 60 per cent of the compact galaxies increase in size further due to renewed star formation and/or mergers.