Relenting to pressure from all sides, Michael Dell agreed Friday to personally pay more to take ownership of the company that bears his name.

Mr. Dell and his partner on the deal, private-equity firm Silver Lake, are now offering a 13-cent special dividend to shareholders, plus a raised price of $13.75 for each share. The increases add $350 million to what had been a $24.4 billion deal for Dell Inc.

In...