Fusion of the outer mitochondrial membrane is mediated by the dynamin-like GTPase mitofusin (MFN). Here, we determined the structure of the minimal GTPase domain (MGD) of human MFN1 in complex with GDP-BeF3-. The MGD folds into a canonical GTPase fold with an associating four-helix bundle, HB1, and forms a dimer. A potassium ion in the catalytic core engages GDP and BeF3- (GDP-BeF3-). Enzymatic analysis has confirmed that efficient GTP hydrolysis by MFN1 requires potassium. Compared to previously reported MGD structures, the HB1 structure undergoes a major conformational change relative to the GTPase domains, as they move from pointing in opposite directions to point in the same direction, suggesting that a swing of the four-helix bundle can pull tethered membranes closer to achieve fusion. The proposed model is supported by results from in vitro biochemical assays and mitochondria morphology rescue assays in MFN1-deleted cells. These findings offer an explanation for how Charcot-Marie-Tooth neuropathy type 2 A (CMT2A)-causing mutations compromise MFN-mediated fusion.