Trump announced the move on Twitter, saying that Pompeo would move to the State Department and that Haspel would "become the new Director of the CIA, and the first woman so chosen. Congratulations to all!"
Jameel Jaffer, formerly deputy legal director of the ACLU, said on his Twitter feed that Haspel is "quite literally a war criminal."
Haspel spent much of her 33-year CIA career in undercover assignments overseas and at CIA headquarters, including serving as the agency's top representative in London and as the acting head of its clandestine service in 2013.
Current and former US intelligence officials who have worked with Haspel praised her as an effective leader who could be expected to stand up to the pressures that Trump has often placed on spy agencies - including his denunciations of the intelligence community's conclusion that Russia interfered in the 2016 election.
Officials described Haspel as a consummate "insider" and said CIA employees would greet her appointment with some relief, because an intelligence veteran would be back in charge.
"The building will love the fact that she's an insider," said Mark Lowenthal, a former senior CIA officer.
Pompeo, a former member of Congress who spent his early career in business, had no profile in the intelligence community apart from his leading role on a congressional committee investigating the terrorist attacks on a US government facility in Benghazi, Libya. Career CIA officers have seen Pompeo as one of the most overtly political directors in the agency's history and a staunch public defender of the President.
Haspel, by contrast, has almost no public profile. But she is a visible presence inside CIA headquarters, running day-to-day operations while Pompeo handles the public-facing aspects of the job, making speeches and media appearances, and meeting with the president.
"This is not someone who has sharp elbows, but she is a sharp competitor," said a former senior intelligence official, who insisted on anonymity to discuss Haspel.