This work reports the results of EPR and NMR study of the Ce3+ incorporation in LaAlO3 single crystals grown by the micro-pulling-down method in the range of the Ce concentrations in the solid solution La1-xCexAlO3 from x = 0.001 up to x = 1.0. From EPR measurements, Ce3+g tensor parameters were determined as a function of Ce concentration. The g tensor has an orthorhombic symmetry even in the trigonal phase (x < 0.1) suggesting that the incorporation of Ce at La site lowers the lattice symmetry near this ion. The local properties of the La1-xCexAlO3 crystals were further studied by 27Al and 139La high-resolution NMR measurements. It was found that 139La chemical shift has the Fermi contact interaction origin. It linearly increases with the Ce concentration from 0 ppm up to 165 ppm at x = 0.5. Due to this strong Fermi contact interaction, separated peaks corresponding to different Ce-O-La spin transfer passways are resolved in the 139La NMR spectra. On the other hand, no Fermi contact interaction is visible in 27Al NMR spectra. However, these spectra contain a satellite peak whose intensity linearly increases with an increase of the Ce concentration leaving position of this peak unchanged. This was interpreted as manifestation of the crystal structure modification in the vicinity of Ce ions in agreement with EPR data. Thus, optical properties of Ce3+ in LaAlO3 will be determined namely by the local crystal structure near this ion.