Disclosed are processes for producing stably transformed fertile wheat a system of transforming wheat via Agrobacterium. This invention provides methods transforming a variety of explants, such as freshly isolated or pre-cultured immature embryos, embryogenic callus and suspension cells. Also disclosed are methods for recovering transgenic plants after transformation within a short period of time, if the explants are regenerable at the time of transformation. Thus the frequency of somaclonal variation associated with prolonged in vitro culture period is significantly reduced. The transformation frequency using this system is comparable to or better than published methods using other systems, such as microprojectile bombardment.