Recent progress in laser-driven plasma acceleration now enables the acceleration of electrons to several gigaelectronvolts. Taking advantage of these novel accelerators, ultrashort, compact, and spatially coherent x-ray sources called betatron radiation have been developed and applied to high-resolution imaging. However, the scope of the betatron sources is limited by a low energy efficiency and a photon energy in the 10 s of kiloelectronvolt range, which for example prohibits the use of these sources for probing dense matter. Here, based on three-dimensional particle-in-cell simulations, we propose an original hybrid scheme that combines a low-density laser-driven plasma accelerator with a high-density beam-driven plasma radiator, thereby considerably increasing the photon energy and the radiated energy of the betatron source. The energy efficiency is also greatly improved, with about 1% of the laser energy transferred to the radiation, and the γ-ray photon energy exceeds the megaelectronvolt range when using a 15 J laser pulse. This high-brilliance hybrid betatron source opens the way to a wide range of applications requiring MeV photons, such as the production of medical isotopes with photonuclear reactions, radiography of dense objects in the defense or industrial domains, and imaging in nuclear physics.