A mechanical product with a finely finished surface and accuracy is a great requirement of current industries and individuals because of its enhanced operational life, reliability, smooth interchangeability, and aesthetic appealing features. Therefore, fine-finishing processes are of extensive importance these days. The magnetorheological (MR) finishing processes are developed where the finishing forces provide uniform forces to a magnetorheological polishing fluid which in turn produces a supergrade finishing. In this study, the rectangular-curved magnet–based MR finishing process was used to superfinish the exterior surface of the cylindrical workpiece of copper material (which is typically used as an electron discharge machine electrode). To ensure the functionality of the current tool, the magnetic simulation was also performed to analyze the magnetic flux distribution within the tool structure, working gap, and workpiece surface. The synthesized MR polishing fluid was applied on the finishing surface of rectangular-curved magnets which further maintained a working gap of 1 mm during the experimentation. The results concluded that the overall 74% roughness change with rectangular-curved magnets (i.e., from initial Ra as 251 nm to final Ra as 66 nm was observed using rotational speed of workpiece as 500 rpm, tool feed as 50 mm/min and 45 min of finishing time), which was more efficient than the existing results of circular-type magnets. Also, the significant improvement in surface texture from the initial to the final finished copper workpiece was confirmed through the scanning electron microscopic images.