Using a recently developed method for in situ high-pressure, laser heating experiments in diamond anvil cells, we obtained a novel post-perovskite phase of SrOsO3. The phase transition from perovskite SrOsO3 was induced at 44 GPa and 1350 K in a diamond anvil cell and characterized with synchrotron powder X-ray diffraction. The newly obtained post-perovskite is quenchable and Le Bail refinements under ambient conditions yielded the unit cell parameters: a = 3.152(9) Å, b = 10.82(2) Å, c = 7.27(1) Å, V = 248.1(1) Å3. In addition, the compression of perovskite SrOsO3 at ambient temperature was investigated up to 66 GPa in a diamond anvil cell using synchrotron powder X-ray diffraction. The compression at ambient temperature showed that pressure alone does not induce the first-order phase transition to the post-perovskite structure. However, at 36 GPa, a continuous phase transition to monoclinic (P21/n) symmetry was detected, persistent up to 58 GPa, where the perovskite transitioned back to orthorhombic (Pbnm) symmetry. Fitting a third-order Birch-Murnaghan equation of state to the obtained P-V data for perovskite SrOsO3 yielded a bulk modulus of K0 = 187.4(15) GPa. Density functional theory calculations were performed to support the experimental findings in the compression study at ambient temperature. This work shows that transformations to the post-perovskite structure can be obtained for a wider range of perovskites than simple empirical rules otherwise suggest.