Magnetic droplets, a class of highly nonlinear magnetodynamic solitons, can be nucleated and stabilized in nanocontact spin-torque nano-oscillators. Here we experimentally demonstrate magnetic droplets in magnetic tunnel junctions (MTJs). The droplet nucleation is accompanied by power enhancement compared with its ferromagnetic resonance modes. The nucleation and stabilization of droplets are ascribed to the double-CoFeB free-layer structure in the all-perpendicular MTJ, which provides a low Zhang-Li torque and a high pinning field. Our results enable better electrical sensitivity in fundamental studies of droplets and show that the droplets can be utilized in MTJ-based applications and materials science.