Dunn will remain an HP director.
The announcement follows two days of meetings of the HP board of directors on the fate of Dunn, who ordered an investigation into leaks to the media of boardroom discussions.
Last week, it was revealed that the investigation included obtaining the phone records of board members and journalists under false pretenses.
The techniques "went beyond what we understood them to be, and I apologize they were employed," Dunn said in a statement.
"She took one for the team," Rob Enderle, of the Enderle Group, told internetnews.com. "She probably would have been voted out as chairperson, anyway," according to Enderle.
Richard Hackborn, a board member since 1992, becomes lead independent director in January, according to HP. Hackborn served as HP chairman in 2000.
Dunn upheld her decision to launch the investigation, saying leaks could affect not only HP's stock, but also that of other companies.
The technique, which is called "pretexting" and involves duping company customer service representatives into divulging account information to those claiming to be account holders, is now banned, according to HP's CEO.
"I am taking action to ensure that inappropriate investigative techniques will not be used again," said Hurd in a statement. "They have no place in HP," according to the CEO.
"HP holds itself to the highest standards of business conduct and we are accountable to these standards for everything that we do," Hurd said in a statement.
Hurd said HP will "work to put these matters behind us so that we fully resume our focus on the business," according to the statement.
"We've focused too much on scandal and investigations and not on operations," Jill Fisch, the T.J. Maloney Professor of Business Law at Fordham Law School, told internetnews.com.
The way revelations have dripped piecemeal from the computer maker has become an obstacle, she added.
Dunn said she plans to continue working toward improving the company's corporate governance standards and resolving the issues involving the HP leak investigation.
That resolution could take time. The scandal has spawned a number of other investigations, including probes by the state of California, the U.S. Justice Department, Congress, the FCC and SEC.
Although Dunn's stepping down as chairwoman will help HP get back on message, there is the danger the pendulum will swing too far the other way, said Fisch.
Internal investigations are becoming an increasingly common tool for companies to confront problems, she said.