Iran has threatened to retaliate. Iraq's prime minister said Washington had violated a deal for keeping U.S. troops in his country.
Israel put its army on high alert and U.S. allies in Europe including Britain, France and Germany voiced concerns about an escalation in tensions.
Soleimani, a 62-year-old general, was regarded as the second most powerful figure in Iran after Supreme Leader Ayatollah Ali Khamenei.
The overnight attack, authorized by President Donald Trump, marked a dramatic escalation in a "shadow war" in the Middle East between Iran and the United States and its allies, principally Israel and Saudi Arabia.