The 2005 US justice department memorandum also showed that Abu Zubaydah, an al Qaeda operative, was waterboarded 83 times, far more than the agency originally said, the Times reported on Sunday.
A former CIA officer had previously said Zubaydah had only been subjected to 35 seconds of waterboarding, which simulates the sensation of drowning.
Some critics have accused Obama of undermining the US intelligence community after he ordered the release of "top secret" memos on interrogation techniques that have largely been condemned as torture.
The US president is due to visit hold private meetings with personnel and to deliver a public message "about the importance of the CIA's mission" to US national security, officials said.
Obama has banned the use of waterboarding and other harsh interrogation techniques, brought in via policies set by the previous US administration under George Bush, the former US president.
Michael Hayden, who was replaced as CIA chief earlier this year by Obama, has defended the agency's methods, saying: "We stand by our story. The critical information we got from Abu Zubaydah came after we began the EIT's [enhanced interrogation techniques]."
He said Zubaydah had "clammed up" after providing some "nominal information" under initial questioning, but under harsher interrogation he "gave up more valuable information" including tips that led to the capture of Ramzi Binalshibh, another senior al Qaeda agent.
Hayden also said the release of top secret memos were "really dangerous" for US intelligence efforts.
"Most of the people who oppose these techniques want to be able to say: 'I don't want my nation doing this', which is a pure honourable position, and 'they didn't work anyway'," he told the Fox News Sunday programme.
"The facts of the case are that the use of these techniques against these terrorists made us safer, it really did," he said.