In a statement, the HP board said Whitman, who herself joined the HP board eight months ago, possesses "additional attributes" to help the company execute its strategy.
"We are at a critical moment, and we need renewed leadership to successfully implement our strategy and take advantage of the market opportunities ahead," said Ray Lane, executive chairman of the board.
Whitman said she supports recent decisions on the strategic direction of the company, but intends to review them in her new capacity.
"I will take a very hard look, but from what I know now the strategy is right," she said in a conference call with analysts.
A strategic decision on the company's Aug. 18 announcement that it will sell or spin off its personal computer business, the Personal Systems Group (PSG), is a high priority, she said.
"In the end, the only way to rebuild confidence in this company is to get results, and that's what I intend to do," Whitman said.
"The best thing we can do is get to a decision on PSG as fast as possible," she said.
She also reaffirmed the company's commitment to its hardware business, including servers and networking equipment.
HP's purchase of the British software company Autonomy will be completed by the end of the year, she said.
"Meg is a technology visionary with a proven track record of execution," Lane said.
"She is a strong communicator who is customer focused with deep leadership capabilities."
Whitman said, "I am honored and excited to lead HP. I believe HP matters -- it matters to Silicon Valley, California, the country and the world."
Lane said the board considered hiring an interim CEO to replace Apotheker, but after considering internal and external candidates, it decided Whitman was "the strongest" person to lead the company.
Lane said the decision to fire Apotheker revolved around concerns about executive team cohesion, execution of strategy and communication to customers and shareholders. He referenced three consecutive quarters of lower-than-expected financial performance.
Board members "very much appreciate" Apotheker's efforts since he joined the company last year, he said.
Apotheker was appointed to head HP last Sept. 30, replacing Mark Hurd. Hurd resigned in August 2010 after the company said it found discrepancies in his expense reporting and investigated sexual harassment allegations against him.