It means the firm no longer has a connection with making PCs or laptops.
Sharp bought 80 percent of Toshiba's personal computing arm in 2018 for $US36m ($NZ54m), and has now bought the remaining shares, Toshiba said in a statement.
Toshiba's first laptop, the T1100, launched in 1985. It weighed 4kg and worked with 3.5 inch floppy disks.
It was launched at first only in Europe with an annual sales target of 10,000 units, according to the Toshiba Science Museum website.