The committee voted behind closed doors Wednesday morning.
The positive review sets her up for a final vote before the full Senate in the coming days. She is all but assured to win Senate confirmation and become the first woman to lead the Central Intelligence Agency.
Haspel currently has the support of the majority of Republicans and endorsements from five Democrats.
The committee's chairman gave her a positive public endorsement after the vote.
“Gina Haspel is the most qualified person the President could choose to lead the CIA and the most prepared nominee in the 70 year history of the Agency,” Chairman Richard Burr, R-N.C., said in a statement. “She has acted morally, ethically, and legally, over a distinguished 30-year career and is the right person to lead the Agency into an uncertain and challenging future. I’m pleased to see the Committee favorably report her nomination to the full Senate, and I look forward to her swift confirmation.”
In the letter, Haspel also acknowledged that it was "a mistake" for the CIA not to have briefed Congress about the program at its inception.
"With the benefit of hindsight and my experience as a senior agency leader, the enhanced interrogation program is not one the CIA should have undertaken," she wrote in the letter to Warner.
"While I won't condemn those that made these hard calls, and I have noted the valuable intelligence collected, the program ultimately did damage to our officers and our standing in the world," Haspel continued.
She had not expressed those feelings publicly, during her contentious confirmation hearing last week. Haspel told the committee that she would not resurrect the agency's controversial rendition, detainee, and interrogation program if she became CIA director, but went no further.
"I don't believe that torture works," she told the committee, but stopped short of saying whether the interrogation program was "immoral" or should have been carried out.
After the vote on Wednesday, many Democrats expressed concern about Haspel's nomination.
Currently serving as the agency's deputy director, Haspel is well-regarded within the agency. She joined the CIA in 1985 and has held a series of high-ranking positions at the intelligence agency throughout her lengthy career, including senior leadership positions within the agency's National Clandestine Service, which oversees the agency's spy operations overseas and its most covert operations programs.
The committee's report on the CIA's rendition program said senior al Qaeda operatives Abu Zubaydah and Abd al-Rahim al-Nashiri were detained at that location.
The report said that while at the black site in Thailand in 2002, Zubaydah was subjected to the controversial practice of waterboarding 83 times and to other "stress" techniques such as being slammed against walls, deprived of sleep and placed in a coffin-sized box for up to 226 hours.
In March, McCain noted that Haspel's CIA career "has intersected with the program of so-called 'enhanced interrogation techniques' on a number of occasions."
"The torture of detainees in U.S. custody during the last decade was one of the darkest chapters in American history," McCain said in a statement. "Ms. Haspel needs to explain the nature and extent of her involvement in the CIA's interrogation program during the confirmation process."