To perform their multiple functions, cilia and flagella are precisely positioned at the cell surface by mechanisms that remain poorly understood. The protist Trypanosoma brucei possesses a single flagellum that adheres to the cell body where a specific cytoskeletal structure is localised, the flagellum attachment zone (FAZ). Trypanosomes build a new flagellum whose distal tip is connected to the side of the old flagellum by a discrete structure, the flagella connector. During this process, the basal body of the new flagellum migrates towards the posterior end of the cell. We show that separate inhibition of flagellum assembly, base-to-tip motility or flagella connection leads to reduced basal body migration, demonstrating that the flagellum contributes to its own positioning. We propose a model where pressure applied by movements of the growing new flagellum on the flagella connector leads to a reacting force that in turn contributes to migration of the basal body at the proximal end of the flagellum.