Dell, founded in 1984, has struggled in the three years since Rollins took over, losing its dominant position in computer sales to Hewlett-Packard, the California-based information technology company, and coming under scrutiny from regulators.
The company's accounting practices are under investigation by US prosecutors after suggestions that the company misstated items in financial reports.
In December, James Schneider, Dell's chief financial officer, suddenly "retired".
Along with announcing the transfer of power, the company lowered its revenue and earnings estimates for its fourth fiscal quarter.
Dell said in a press release that the firm "has tremendous opportunities ahead of it" and said he was optimistic about the company's prospects going forward.
Nunn said: "The board believes that Michael's vision and leadership are critical to building Dell's leadership in the technology industry for the long term."
Dell created the company with $1,000 and served as CEO from its inception until he handed the reins to Rollins in 2004.
The company shipped the firm's computers directly to users, eliminating stores and "middle men" and cutting costs.
While attending a Texas university, Dell established a computer company that he ran from his room. He later dropped out of college, borrowed money from family and turned his his computer company into one of the most profitable in the world with billions of dollars in annual revenues.
Industry publications have since proclaimed Dell "Man of the Year" and "Entrepreneur of the Year" and at one point his company was declared the most admired in the world by Fortune magazine.