Spin-polarized current can excite the magnetization of a ferromagnet through the transfer of spin angular momentum to the local spin system. This pure spin-related transport phenomenon leads to alluring possibilities for the achievement of a nanometer scale, complementary metal oxide semiconductor-compatible, tunable microwave generator that operates at low bias for future wireless communication applications. Microwave emission generated by the persistent motion of magnetic vortices induced by a spin-transfer effect seems to be a unique manner to reach appropriate spectral linewidth. However, in metallic systems, in which such vortex oscillations have been observed, the resulting microwave power is much too small. In this study, we present experimental evidence of spin-transfer-induced vortex precession in MgO-based magnetic tunnel junctions, with an emitted power that is at least one order of magnitude stronger and with similar spectral quality. More importantly and in contrast to other spin-transfer excitations, the thorough comparison between experimental results and analytical predictions provides a clear textbook illustration of the mechanism of spin-transfer-induced vortex precession.