Plasma turbulence is a ubiquitous dynamical process that transfers energy across many spatial and temporal scales in astrophysical and space plasma systems1-8. Although the theory of anisotropic magnetohydrodynamic (MHD) turbulence has successfully described phenomena in nature, 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 confirmed9-10. Here we report the first observational evidence for the Alfvénic weak-to-strong transition in MHD turbulence in the terrestrial magnetosheath using the four Cluster spacecraft. The observed transition indicates the universal existence of strong turbulence regardless of the initial level of MHD fluctuations. Moreover, the observations demonstrate that the nonlinear interactions of MHD turbulence play a crucial role in the energy cascade, widening the directions of the energy cascade and broadening the fluctuating frequencies. Our work takes a critical step toward 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.