A transverse mode switchable all-fiber Brillouin laser architecture is proposed. This laser architecture consists mainly of an optical switch, a set of cascaded mode selection couplers (MSCs), and a few-mode fiber ring cavity. By switching the output signal of the optical switch, specific transverse modes generated by MSCs can be coupled into the ring cavity to excite the corresponding Brillouin scattering light. Based on the Brillouin nonlinear effect, the desired mode resonant amplification is guaranteed, and a transverse mode switchable laser beam is obtained. As a proof of principle, we have implemented an all-fiber Brillouin laser with switchable output of fundamental transverse (LP01) mode and second-order transverse (LP11) mode at the wavelength of 1550 nm. The slope efficiency and linewidth for LP01 and LP11 modes are 25.1% and 4.9 kHz, 20.9% and 4.96 kHz, respectively. Additionally, the orbital angular momentum laser beam with l=+1, -1, or 0 switchable output is also demonstrated from our all-fiber Brillouin laser system. Owing to the compact all-fiber architecture, this transverse mode switchable Brillouin fiber laser is reliable during long-term operation and thus promising for many practical applications.