We present a resonant x-ray scattering study at the manganese K edge on La_7/8Sr_1/8MnO₃ at temperatures between 10 K and 310 K along with thermal expansion, magnetization, and electrical resistivity measurements. At the Mn K edge the symmetry-forbidden (300) reflection is observed in the whole temperature range under investigation and its integrated intensity is found to be directly connected to structural distortions. In particular, the intensity of the (300) reflection increases strongly in the cooperative Jahn-Teller distorted phase between 150 K and 270 K. The increase of the resonant intensity in this temperature regime, the rotation of the beam polarization from σ to π, the sin²-azimuthal dependence and the anomalies displayed by the lattice constants give firm experimental evidence for an orbital ordered state between 150 K and 270 K similar to that found in LaMnO₃. Upon cooling, the intensity of the (300) reflection collapses at the charge ordering temperature T_CO=150K and the resonant (1.5,1.5,3) superstructure reflection emerges. This reflection also displays a resonant behavior at the Mn K edge and a pronounced azimuthal dependence. However, a resonant signal is observed in the σσ as well as in the σπ channel. The results reveal that the metal-insulator transition of La_7/8Sr_1/8MnO₃ is accompanied by an orbital reordering.