The activist investor is also taking a leave of absence from his investment company, Relational Investors.
The company said its board of directors will discuss appointing a new chairman at its next board meeting.
Whitworth, who was appointed chairman on an interim basis in April 2013, has been a member of the HP board of directors since 2011. He is co-founder and principal of Relational Investors LLC, a registered investment advisor founded in 1996.
What is Hewlett-Packard's stock doing now?
"Ralph has been a friend and close advisor to me, the HP leadership team and every member of the board for nearly three years," said Meg Whitman, president and chief executive officer, HP, said in a statement. "He has been a wonderful contributor to our efforts to turn HP around. Ralph's passion and incredible mind for business will be deeply missed by all of us. We wish Ralph and his family the very best."