Spontaneous formation of solitary wave structures has been observed in Earth’s magnetopause, and is shown to be caused by the breakup of a zonal flow by the action of drift wave turbulence. Here we show matched observations and modeling of coherent, large-scale solitary electrostatic structures, generated during the interaction of short-scale drift wave turbulence and zonal flows at the Earth’s magnetopause. The observations were made by the Cluster spacecraft and the numerical modeling was performed using the wave-kinetic approach to drift wave-zonal flow interactions. Good agreement between observations and simulations has been found, thus explaining the emergence of the observed solitary structures as well as confirming earlier theoretical predictions of their existence.