Dunn, who took over last year as non-executive chairwoman after the stormy reign of Carly Fiorina, apologised after private detectives that were hired by herself to investigate boardroom leaks to the media "went beyond" their mandate.
Dun said: "Unfortunately the investigation, which was conducted with third parties, included certain inappropriate techniques. These went beyond what we understood them to be, and I apologise that they were employed."
The company said that it was co-operating fully with the inquiries but Dunn has denied authorising illicit tactics.
The private investigation identified a board member as the suspected leak, but did so by getting telephone records with a ruse known as "pretexting" - calling the telecom company and posing as customers.
HP said that Mark Hurd, the company's chief executive officer and president, would succeed Dunn as chairman at a board meeting on January 18. Dunn will continue to serve as a director.
Hurd said he was "taking action to ensure that inappropriate investigative techniques will not be employed again", adding that "They have no place in HP."
While no law on the California books specifically outlaws "pretexting", state prosecutors believe the deception violated laws regarding identification theft and unauthorised access to computer data.
Silicon Valley venture capitalist Thomas Perkins, who resigned from the HP board in protest at the leak probe tactics, had called for Dunn to resign.
Dunn said Perkins advocated strong investigative techniques such as lie detector tests, and that his change of heart came only after the leaker was identified as his friend, George Keyworth.
Keyworth announced on Tuesday that he was also resigning from the board. He admitted to being the source of a CNET.com article about HP in January, but denied that his comments involved "the disclosure of confidential or damaging information".
Unlike its rival Dell, HP has posted strong earnings growth this year and its share price has climbed about 30 per cent since Fiorina's departure. HP's stock closed Tuesday up 1.54 per cent at $36.92.