The firm said it had signed "a definitive merger agreement" that gives shareholders $13.65 (£8.70) per share in cash - a premium of 25% over Dell's January 11 closing share price.
"I believe this transaction will open an exciting new chapter for Dell, our customers and team members," Mr Dell said.
Dell shares dropped 2.6% to $13.27 on the Nasdaq after the plan was announced.
The move, which would de-list the company from stock markets, could ease some of the pressure on Dell, which is cash-rich but has been seeing profits slump.
The Texas-based computer maker, which Mr Dell started in his college dormitory room, once topped a market capitalisation of $100bn (£63bn) as the world's biggest PC producer.
The plan is subject to several conditions, including a vote of unaffiliated stockholders.
It calls for a "go shop" period to allow shareholders to determine if there is a better offer.
"We can deliver immediate value to stockholders, while we continue the execution of our long-term strategy and focus on delivering best-in-class solutions to our customers as a private enterprise," Mr Dell said of the plan.
Dell was a pioneer of phone-ordered, custom built PCs in Britain during the 1990s.
The company worked from facilities in the Irish Republic, Britons were able to specify their hard and software requirements before machines were delivered to their home.