President Donald Trump’s pick to lead the Central Intelligence Agency will tell the Senate Intelligence Committee Wednesday that, if she is confirmed, the agency won’t restart interrogation programs such as those used on detainees after the Sept. 11, 2001, terrorist attacks, according to her prepared testimony.

Gina Haspel, the first woman nominated to lead the CIA, is expected to be asked at her confirmation hearing Wednesday about a number of controversial episodes from her career at the agency, in particular her participation...