WASHINGTON—Mullah Mohammad Omar, the founder of the Taliban, lived in hiding near a U.S. base in southern Afghanistan until his death, according to a new research-group report that contradicts long-held theories by U.S. officials about the notorious one-eyed leader.

The consensus among experts, including at the Central Intelligence Agency, was that Mullah Omar fled to Pakistan after the U.S. ousted the Taliban following the Sept. 11 terrorist attacks orchestrated by al Qaeda, which operated in Afghanistan under the Taliban’s...