When Michael S. Dell took his namesake technology company private in 2013, he said that doing so would give him the freedom to prepare it for a future that stretched well beyond personal computers.

Having expanded Dell into a huge one-stop technology shop for businesses, he and his financial partner, the investment firm Silver Lake, plan to bring the company back to the public markets — albeit in a complicated fashion that keeps them firmly in control.

Mr. Dell and Silver Lake are expected to announce as early as Monday that they have struck a $21.7 billion deal to buy out investors in a special class of shares created in 2016 to help Dell buy the networking company EMC. That stock effectively tracks the performance of Dell’s 82 percent stake in VMware, the fast-growing network software company that Dell inherited when it bought EMC. (The other 18 percent of VMware is publicly traded as a different stock.)

The deal, which was approved by the boards of Dell and VMware on Sunday evening, would simplify the stock structure of Dell and its publicly traded subsidiary. But it would also mark the return of Dell to the public markets, with a twist: The special shares held by Mr. Dell and Silver Lake would give them more votes than other investors.