The solar radiation in the cores of the MgII h and k spectral lines plays a significant role in the illumination of prominences, coronal mass ejections (CMEs), spicules, flare loops, and surges. Moreover, the radiation in these lines strongly correlates with solar magnetic activity and the ultraviolet solar spectral irradiance affecting the photochemistry, especially of oxygen and nitrogen, in the middle atmosphere of the Earth. This work provides a data-driven model of temporal evolution of the solar full-disk MgII h and k profiles over the solar cycle. The capability of the model to reproduce the MgII h and k profiles for an arbitrary date is statistically assessed. Based on selected 76 IRIS near-UV full-Sun mosaics covering almost the full solar cycle 24, we find the parameters of double-Gaussian fits of the disk-averaged MgII h and k profiles and a model of their temporal evolution parameterized by the Bremen composite MgII index. The model yields intensities within the uncertainties of the observed data in more than 90% of the reconstructed profiles assuming a statistically representative set of Bremen MgII index values in the range of 0.150-0.165. The relevant full-disk MgII h and k calibrated profiles with uncertainties and spectral irradiances are provided as an online machine-readable table. The model yields MgII h and k profiles representing the disk incident radiation for the radiative-transfer modeling of prominences, CMEs, spicules, flare loops, and surges observed at arbitrary time.