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The emerging field of nanomagnonics utilizes high‐frequency waves of magnetization—spin waves—for the transmission and processing of information on the nanoscale. The advent of spin‐transfer torque has spurred significant advances in nanomagnonics, by enabling highly efficient local spin wave generation in magnonic nanodevices. Furthermore, the recent emergence of spin‐orbitronics, which utilizes spin–orbit interaction as the source of spin torque, has provided a unique ability to exert spin torque over spatially extended areas of magnonic structures, enabling enhanced spin wave transmission. Here, it is experimentally demonstrated that these advances can be efficiently combined. The same spin–orbit torque mechanism is utilized for the generation of propagating spin waves, and for the long‐range enhancement of their propagation, in a single integrated nanomagnonic device. The demonstrated system exhibits a controllable directional asymmetry of spin wave emission, which is highly beneficial for applications in nonreciprocal magnonic logic and neuromorphic computing.