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Plasma turbulence is a ubiquitous dynamical process that transfers energy across many spatial and temporal scales in astrophysical and space plasma systems. Although the theory of anisotropic magnetohydrodynamic (MHD) turbulence has successfully described natural phenomena, its core prediction of an Alfvénic transition from weak to strong MHD turbulence when energy cascades from large to small scales has not been observationally confirmed. Here we report the first observational evidence for the Alfvénic weak-to-strong transition in MHD turbulence in Earth's magnetosheath using data from four Cluster spacecraft. Our observations demonstrate the universal existence of strong turbulence accompanied by the initial state of weak turbulent fluctuations. Moreover, we find that the nonlinear interactions of MHD turbulence are crucial to the energy cascade, widening the cascade directions and broadening the fluctuating frequencies. Our work takes a critical step forward in understanding the complete picture of turbulence cascade, connecting the weak and strong MHD turbulence systems. It will have broad implications in star formation, energetic particle transport, turbulent dynamo, and solar corona or solar wind heating.