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We report on the evolution of the number density and size of early-type galaxies (ETGs) from z ~ 2 to z ~ 0. We select a sample of 563 massive (M > 1010 M⊙), passively evolving (specific star formation rate <10-2 Gyr-1), and morphologically spheroidal galaxies at 0 < z < 2.5, using the panchromatic photometry and spectroscopic redshifts available in the Great Observatories Origins Deep Surveys fields. We combine Advanced Camera for Surveys and Wide Field Camera 3 Hubble Space Telescope images to study the morphology of our galaxies in their optical rest frame in the entire 0 < z < 2.5 range. We find that throughout the explored redshift range the passive galaxies selected with our criteria have weak morphological K-correction, with size being slightly smaller in the optical than in the UV rest frame (by ~20% and ~10% at z > 1.2 and z < 1.2, respectively). We measure a significant evolution of the mass-size relation of ETGs, with a fractional increment that is almost independent of the stellar mass. ETGs formed at z > 1 appear to be preferentially small, and the evolution of the mass-size relation at z < 1 is driven by both the continuous size growth of the compact galaxies and the appearance of new ETGs with large sizes. We also find that the number density of all passive ETGs increases rapidly, by a factor of five, from z ~ 2 to z ~ 1, and then more mildly by another factor of 1.5 from z ~ 1 to z ~ 0. We interpret these results as evidence that the bulk of the ETGs are formed at 1 < z < 3 through a mechanism that leaves very compact remnants. At z < 1 the compact ETGs grow gradually in size, becoming normal-size galaxies, and at the same time new ETGs with normal-large sizes are formed. [ABSTRACT FROM AUTHOR]