Johnson was not available to comment on his new position. Officials at Blackstone could not be reached.
During his three years at the computer maker, Johnson oversaw some 20 acquisitions worth about $10 billion, according to Frink.
He oversaw the 2009 purchase of Perot Systems, which catapulted Dell into the technology services market alongside IBM and Hewlett-Packard. Other deals during his tenure included Quest Software, SecureWorks, SonicWall, and Wyse Technology.
Rival Hewlett-Packard has had to take large write-offs for several acquisitions, including outsourcing services provider EDS and data analytics firm Autonomy. Dell has proven more circumspect, analysts say, at one point ceding to HP after a bidding war drove up the price of a data storage firm that both were eyeing.
Shannon Cross, an analyst with Cross Research, said Johnson built an infrastructure at Dell that is adept at identifying acquisition targets and integrating them into the company.
"Dell has successfully used Johnson's team to expand its IP and product portfolio," she said.
Johnson, who reported directly to Michael Dell, will be replaced by two vice presidents who will report to the company's chief financial officer, Brian Gladden.
"He leaves a strong and sustainable organization behind, one that will continue to execute our strategy and pursue our aggressive M&A activities," Frink said in a statement.
He is leaving at a tough time for Dell. Its stock has tumbled 30 percent over the past year, while the Nasdaq Composite Index has climbed 16 percent.
Dell's hardware sales have fallen as it has struggled to develop mobile devices to compete with Apple's iPhone and iPad, as well as smartphones and tablets running on Google's Android operating system.
Business customers have generally cut back on buying of hardware from Dell and other suppliers in recent months until the economy shows new signs of strength.
In its most recent quarter, the company reported a 47 percent drop in quarterly profit. Once the world's largest maker of PCs, it has fallen to the No. 3 spot, behind Lenovo and Hewlett-Packard.
Vice President Chris Kleiman was named to run Dell's M&A team, while Vice President Prakash Jothee was picked to head up its corporate strategy team.