Aims. In this paper we discuss the age and spatial distribution of young (age < 1 Gyr) Small Magellanic Cloud (SMC) and Large Magellanic Cloud (LMC) clusters using data from the Magellanic Cloud Photometric Surveys. Luminosities are calculated for all age-dated clusters. Methods. The ages of 324 and 1193 populous star clusters in the SMC and the LMC were determined fitting Padova and Geneva isochrone models to their resolved color-magnitude diagrams. The clusters cover an age range between 10 Myr and 1 Gyr in each galaxy. For the SMC, a constant distance modulus of = 18.90 and a metallicity of Z = 0.004 were adopted. For the LMC, we used a constant distance modulus of = 18.50 and a metallicity of Z = 0.008. For both galaxies, we used a variable color excess to derive the cluster ages. Results. We find two periods of enhanced cluster formation in both galaxies at 160 Myr and 630 Myr (SMC) and at 125 Myr and 800 Myr (LMC). We present the spatially resolved recent star formation history of both Clouds based on young star clusters. The first peak may have been triggered by a close encounter between the SMC and the LMC. In both galaxies, the youngest clusters reside in the supergiant shells, giant shells, the intershell regions, and toward regions with a high Hα content, suggesting that their formation is related to expansion and shell-shell interaction. Most of the clusters are older than the dynamical age of the supergiant shells. No evidence of cluster dissolution was found. Computed V band luminosities show a trend toward fainter magnitudes with increasing age, as well as a trend toward brighter magnitudes with increasing apparent cluster radii.