Haspel was named acting head of CIA National Clandestine Service in 2013 but she was shifted from her position in a very short time because of her worrisome direct role in post-September 11 interrogation operations, which included many methods of torture - such as Trump's favorite waterboarding.
During his confirmation hearing, Pompeo said he would "absolutely not" restart the use of illegal interrogation techniques.
The Trump administration denied that the draft order that news organizations, including The Associated Press, obtained last week was an official White House document.
Mr Trump has often spoken of his belief that "torture works" and that the USA should be willing to make use of techniques such as waterboarding in its efforts against militant groups such as Isis.
Haspel briefly ran a secret CIA prison where accused terrorists Abu Zubayadah and Abd al Rahim al-Nashiri were waterboarded in 2002, according to current and former USA intelligence officials, who spoke earlier to The Associated Press on condition of anonymity. She helped carry out an order to destroy videotapes of the waterboarding, which simulates drowning and is considered a form of torture, these people said.
The Justice Department spent several years investigating alleged abuses in the interrogation program and the destruction of the tapes, but no charges were ever filed.
Pompeo and Defense Secretary James Mattis have both rejected the so-called "enhanced interrogation techniques". "Does torture work?' And the answer was 'Yes, absolutely", he said.
Christopher Anders, the deputy director of the Washington office of the American Civil Liberties Union, said he was "gravely concerned" about CIA Director Mike Pompeo's decision to pick Haspel as his deputy. The document said US laws should be obeyed at all times and explicitly rejects "torture", but does not address the possibility that Trump might seek to change the law or rewrite the Army Field Manual, which lays out interrogation methods that can be used. "Moreover, I can't imagine that I would be asked that" by the president. But he also said he'd consult with CIA and other government experts on whether current restrictions were an "impediment to gathering vital intelligence to protect the country or whether any rewrite of the Army Field Manual is needed".
"Haspel's selection drew praise from former senior intelligence officials, with ex-National Intelligence Director James Clapper saying: "[Haspel] has the broad-gauged experience from both foreign and domestic assignments to serve as the right-arm for Director [Mike] Pompeo". She will be the first career female officer appointed to the position.