The structure of the NGC 6251 jet on the milliarcsecond scale is investigated using images taken with the European VLBI Network and the Very Long Baseline Array. We detect a structural transition of the jet from a parabolic to a conical shape at a distance of (1-2)x10^5^ times the Schwarzschild radius from the central engine, which is close to the sphere of gravitational influence of the supermassive black hole (SMBH). We also examine the jet pressure profiles with the synchrotron minimum energy assumption to discuss the physical origin of the structural transition. The NGC 6251 jet, together with the M87 jet, suggests a fundamental process of structural transition in the jets of active galactic nuclei (AGNs). Collimated AGN jets are characterized by their external galactic medium, showing that AGN jets interplay with the SMBH and its host galaxy.