The Islamic State runs a self-sustaining economy across territory it controls in Syria and Iraq, pirating oil while exacting tribute from a population of at least eight million, Arab and Western officials said, making it one of the world's richest terror groups and an unprecedented threat.

That illicit economy presents a new picture of Islamic State's financial underpinnings. The group was once thought to depend on funding from Arab Gulf donors and donations from the broader Muslim world. Now, Islamic State—the former branch...