The spin-helical Dirac fermion topological surface states in a topological insulator nanowire or nanoribbon promise novel topological devices and exotic physics such as Majorana fermions. Here, we report local and non-local transport measurements in Bi2Te3 topological insulator nanoribbons that exhibit quasi-ballistic transport over similar to 2 mu m. The conductance versus axial magnetic flux F exhibits Aharonov-Bohm oscillations with maxima occurring alternately at half-integer or integer flux quanta (Phi(0) = h/e, where h is Planck's constant and e is the electron charge) depending periodically on the gate-tuned Fermi wavevector (k(F)) with period 2 pi/C (where C is the nanoribbon circumference). The conductance versus gate voltage also exhibits k(F)-periodic oscillations, anti-correlated between Phi = 0 and Phi(0)/2. These oscillations enable us to probe the Bi2Te3 band structure, and are consistent with the circumferentially quantized topological surface states forming a series of one-dimensional subbands, which undergo periodic magnetic field-induced topological transitions with the disappearance/appearance of the gapless Dirac point with a one-dimensional spin helical mode.