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 evidence for the Alfvénic weak-to-strong transition in small-amplitude, turbulent MHD fluctuations in Earth’s magnetosheath using data from four Cluster spacecraft. Our observations demonstrate the universal existence of strong turbulence accompanied by weak turbulent fluctuations on large scales. Moreover, we find that the nonlinear interactions of MHD turbulence are crucial to the energy cascade, as they broaden the cascade directions and fluctuating frequencies. The observed connection between weak and strong MHD turbulence systems may be present in many astrophysical environments, such as star formation, energetic particle transport, turbulent dynamos, and solar corona or solar wind heating.