A pair of transverse wobbling bands is observed in the nucleus ^{135}Pr. The wobbling is characterized by ΔI=1, E2 transitions between the bands, and a decrease in the wobbling energy confirms its transverse nature. Additionally, a transition from transverse wobbling to a three-quasiparticle band comprised of strong magnetic dipole transitions is observed. These observations conform well to results from calculations with the tilted axis cranking model and the quasiparticle rotor model.