The microstructure evolution during dissimilar friction stir welding of copper with stainless steel 316L is studied. The welding is performed in transparence configuration using tools of two different geometries. The joints are characterized by optical microscopy, scanning and transmission electron microscopy, electron backscattered diffraction, and microhardness. The microstructure and crystallographic texture of base metals are significantly affected. The joint produced using a shoulder of 8 mm in diameter is characterized by a copper nugget with refined grains. The texture of copper is dominated by component of the shear texture. The steel beneath the tool shows a grain refinement with grains of sub‐micron size and a texture which is close to the ideal simple shear texture. For the joint produced by the 16 mm diameter tool shoulder, the nugget consists of large grains of copper, while the steel beneath the tool shows small recrystallized grains of micrometer size. The texture in the steel is dominated by the component of the shear texture. The Cu/316L interface in both types of joint is of very good quality. In a detailed study of the interface, it is revealed that the welding of metals is achieved by mutual intense mechanical interlocking without formation of any intermetallic compounds.