We have studied the phase transformation of forsterite to wadsleyite under shear stress at the Earth's transition zone pressure and temperature conditions. Two-step experiments were performed using a multi-anvil press. First, we hot pressed iron-free forsterite at 6 or 11 GPa and 1100 degrees C. Then we deformed a slab of this starting material using a direct simple shear assembly at 16 GPa and 1400 degrees C for 1, 15, 35, 40, or 60 min. Both the starting material and the deformed samples were characterized using optical and scanning electron microscopy including measurements of crystal preferred orientations (CPO) by electron back scattered diffraction (EBSD), transmission electron microscopy (TEM), and Fourier transform infrared spectroscopy (FTIR). The phase transformation occurs very rapidly, in less than 1 min, and metastable forsterite relics are not observed after deformation. The grain size of wadsleyite is slightly smaller than the forsterite starting material. The water contents obtained from FTIR analyses in forsterite and wadsleyite are 65-124 wt ppm H2O and 114-736 wt ppm H2O, respectively, which are well below water solubility at similar conditions in the presence of free water. Wadsleyite aggregates display weak CPO patterns with [1 0 0] axes concentrated at low angle to the shear direction, [0 1 0] axes perpendicular to the shear plane and nearly random [0 0 1] axes. Only a few dislocations were observed in wadsleyite with TEM. This observation is consistent with the assumption that most dislocations formed during the initial high-stress stages of these stress-relaxation experiments, were consumed in the phase transformation, probably enhancing the transformation rate. CPO patterns vary as a function of the water content: with increasing water content the density of [1 0 0] axes parallel to the shear direction decreases, and the density of [0 0 1] axes increases. Viscoplastic self-consistent modeling of CPO evolution using previously reported glide systems for wadsleyite, i.e., [1 0 0]{0 k 1} and 1/2 (1 1 1){1 0 1}, cannot reproduce the measured CPO, unless the [0 0 1](0 1 0) system, for which dislocations have not been observed by TEM, is also activated. In addition, wadsleyite grain growth suggests the participation of diffusion-assisted processes in deformation. Calculated anisotropies for P and S-waves using measured CPO are always below 1%. This very low anisotropy is due to both the low finite strain achieved in the experiments, which leads to weak wadsleyite CPO, and to the diluting effect of added majorite. The present experiments emphasize the importance of stress, grain size evolution and water content in the forsterite to wadsleyite phase transformation and subsequent deformation in the transition zone.