The structural phase transition in the orthovanadates LaVO3 and CeVO3 has been studied with high energy synchrotron x-ray diffraction. LaVO3 undergoes a second order phase transition at T-N=143 K and a first order transition at T-t=141 K, while in CeVO3 there are phase transitions occurring at T-0=154 K of second order and at T-N=134 K of first order. These phase transitions are confirmed by specific heat measurements. The phase transition at T-t in LaVO3 or T-0 in CeVO3 is due to a G- type orbital ordering which lowers the structure symmetry from orthorhombic Pbnm to monoclinic P2(1)/b11. The structure change at T-N in CeVO3 is ascribed to an orbital ordering enhanced magnetostrictive distortion, while that at T-N in LaVO3 is most probably due to an ordered occupation of the vanadium 3d t(2g) orbitals associated with an antiferromagnetic ordering. We propose that the first order phase transition at T-t in LaVO3 should be associated with a sudden change of both spin and orbital configurations, similar to the phase transition at T- s=77 K in YVO3 [Ren et al., Nature (London) 396, 441 (1998)], causing a reversal of the net magnetization. However, the ordered state above T-t in LaVO3 is identical to that below T-s in YVO3. It is found that, with increasing lanthanide ionic radius, the Neel temperature T-N increases while the orbital ordering onset temperature decreases in these orthovanadates.