TOKYO—Toshiba Corp., which was the first in the world to commercialize laptop computers in 1985, is selling the business to Sharp Corp., a symbolic step marking Toshiba’s withdrawal from most consumer businesses.

Sharp is paying just ¥4 billion ($36 million) for an 80.1% stake in a business that once was at the forefront of the global move toward mobile computing. Osaka-based Sharp, controlled by Taiwan-based iPhone assembler Foxconn Technology Group, has been expanding its consumer goods lineup because Foxconn wants to establish...